Ches Sudoku

Chessudoku

Chessudoku

Matthew Skala

c 2006 Matthew SkalaAll rights reserved except as provided by the below license

CC BY: $This document is licensed under the Creative Commons Attribution–NonCommer-cial–ShareAlike 2.5 Canada License. To view a copy of this license, visit http:

//creativecommons.org/licenses/by-nc-sa/2.5/ca/ or send a letter to CreativeCommons, 559 Nathan Abbott Way, Stanford, California 94305, USA.

First printed/eBook edition

PrefaceI had the idea for this book when I read an article by Ed Pegg, Jr.

on the Mathematical Association of America Web site.1 He pro-

posed a set of rules for “Chess Sudoku” somewhat different from

the rules I use, but while I was investigating the possibilities of

puzzles using his rules, I had ideas for several other kinds of

number-placement puzzles using chess pieces and some of those

are included here. Generating the puzzles proved to be so addic-

tive that I spent a lot of time on it I really should have spent doing

other things (like working on my PhD thesis); part of the reason

for publishing this book is to redeem that time, and maybe make

some money from it.

The puzzles are generated by a combination of human design

and computer search. I use a customized solver written using the

CHR constraint logic system on top of SWI-Prolog; the solver is

several orders of magnitude slower than the current state of the

art in high-speed computer Sudoku solvers, but it has the big ad-

vantage of easy customizability for rule variations. The general

approach for making a puzzle is to start with a random solution

and then erase cells as far as possible without creating alternate

solutions. I modify the process a little to make symmetric puzzles,

and run each finished puzzle through the solver a second time to

confirm that it has exactly one solution and get a difficulty esti-

mate.

Re-checking is also important because I am constantly modify-

ing the software to take into account new rule variations and so-

lution techniques, so I sometimes have puzzles lying around that

may have been based on incorrect logic from experimental soft-

ware versions. Each rule variant raises different technical chal-

lenges for the computer solver, and it often takes several rewrites

1http://www.maa.org/editorial/mathgames/mathgames_09_05_05.

html

5

6 Preface

to tune the solver to a variant.

After generating a list of puzzles containing up to twice as

many as I actually want, I go through and manually select the

ones that look best for inclusion in the book. A few minutes to an

hour of computer time goes into each finished puzzle; the entire

book, taking into account puzzles that were generated but not

used, took several weeks. The amount of human labour is hard

to estimate, but roughly corresponds to my spare time for that

period.

I am seriously considering publishing some of my other work

through Lulu.com too, so this book is also intended to serve as a

trial run for other projects. If you like it and would like to see

others, please let me know. Would you like more Chessudoku

puzzles? More of other kinds of puzzles? A Pimpmaster C finance

textbook? A collection of short stories? Astrological notes and

an ephemeris for the minor planet 2202 Pele? Those are just a

few of the projects I’m considering—but whether they’re worth

doing depends on whether people will buy them. I will be setting

up a Web site for this volume at http://ansuz.sooke.bc.ca/

books/chessudoku/ to collect comments and suggestions. Some

of the puzzles in this book, and others of a similar nature, are

also included in the pool for my “Matt’s Puzzle Corner” daily Web

site feature at http://ansuz.sooke.bc.ca/sudoku/, so you may

want to subscribe to that for an ongoing supply.

You may notice that this book is published under a Creative

Commons license. Although I am charging a fee for the copies

I sell through Lulu, you may be able to find someone who has

already bought one and is willing to let you duplicate it (especially

easy with the electronic edition), and that’s perfectly legal. The

one significant reason you might want to pay for it anyway, even

if you can get it free, is that I only get paid if you pay me, and the

more I get paid, the more likely I am to write other books.

This book was typeset with the LATEX typesetting system and

these typefaces:

• Charter by Matthew Carter for the main text;

• Avant Garde by Herb Lubalin for headings;

Preface 7

• Augie by Steven J. Lundeen for script numerals in puzzles;

• KqNb [Skak New] by Ulrich Dirr for chess symbols;

• ✯❖✔❂ [Zapf Dingbats] by Hermann Zapf for, surprisingly

enough, dingbats; and

• Computer Modern by Donald Knuth for URLs and a few ad-

ditional symbols like “×”.

The cover background image is a Volterra-Lotka fractal gener-

ated by xfractint, using the atan and tdis colouring options.

The chess position is the final position from the 11 May 1997

game between the human World Chess Champion Garry Kasparov

(Black) and the IBM computer Deep Blue (White). Kasparov’s

spectacular 19-move loss of that game, and so the match, was

a landmark event in the history of the human relationship with

artificial intelligence.

❧ ❀ ❧

I. White King KThe White King invited the Black King to tea in the Sudoku gar-

den. After they refreshed themselves, the talk turned (as it often

did with these two) to military matters. They debated ways to

avoid the problem of friendly fire, and the White King summoned

some of his knights to demonstrate his own special way of deploy-

ing his forces.

N

N

N

N

N

N

N

N

N

“As you can see, old chap,” he said to the Black King, “I’ve

arranged nine knights on the 81 squares of the Sudoku garden in

such a way that no two knights are in the same horizontal rank or

vertical file. Furthermore, no knight can reach any other knight

by a chess knight’s move of two squares horizontally or vertically

9

10 K

followed by one more square at right angles. Thus, it’s impossible

for them to attack each other by mistake.”

“I see something else that piques my interest,” said the Black

King. “One of your children was playing here earlier and left num-

bers chalked on the pavement. You happen to have placed your

knights on all the 9s in the solution to a Sudoku puzzle, and the

remaining numbers 1 to 8 still form something like a Sudoku so-

lution.” It was true: every rank, file, and marked-off 3×3 block

of the Sudoku garden contained each of the digits 1 to 8 exactly

once, as well as one White knight.

1 6 4 2 N 5 8 3 72 N 7 3 4 8 1 6 53 5 8 7 6 1 4 N 2

8 3 6 4 1 2 5 7 N7 1 N 5 8 6 3 2 44 2 5 N 7 3 6 1 8

N 8 2 1 3 4 7 5 66 7 3 8 5 N 2 4 15 4 1 6 2 7 N 8 3

After some more experimentation and a lot of chalking and

rubbing-out of figures on the ground, the kings determined that it

wouldn’t always work: if you played Sudoku in the ordinary way,

quite often you’d end up with two 9s a knight’s move apart, so you

couldn’t replace all the 9s with White knights and always have

them unable to attack each other. But they found many puzzles

where it did work, and here are some of them.

K 11

These puzzles are similar to the popular Sudoku puzzles you

may be familiar with: given a grid with some squares already

marked, you must fill in the numbers and White knights so that

every rank, file, and marked-off 3×3 block in the grid contains

each digit from 1 to 8 once, and one White knight. However, no

two knights can be a chess knight’s move apart; and you will need

to use that fact in order to solve the puzzles. Even if there are no

White knights visible in the clues, you’ll still need to be aware of

the rule regarding their placement, in order to solve the puzzles.

As in regular Sudoku, there is a solution for every puzzle and

only one solution for every puzzle. The solutions are at the back

of the book, in randomized order so that you can look up just one

without accidentally seeing the solution for the next puzzle. Each

puzzle is labelled with the page number of the solution. But you

should be able to find the solutions by logic, based on the clues

you are given. It is traditional to outlaw “guessing,” but nobody

has been able to give me a convincing explanation of what that

actually means, so there’s no point saying it. Guess if you want to.

The puzzles are arranged in increasing order of difficulty, from

easy to nearly impossible, according to a computer analysis of

their difficulty that may or may not be accurate. Ratings below

200 are considered “easy” and ratings above 300 are very hard;

ratings in between are suitable for intermediate players. Don’t be

fooled by the number of “given” squares. That has almost nothing

to do with how difficult each puzzle may be.

Oh—and if you have trouble drawing the little pictures of

knights, you’re welcome to just use the letter “N” instead. That’s

what I do. Don’t use “K” because it’ll cause confusion later. To

coin a phrase, “Save your ‘K,’ Reader, there’s kings!”

❧ K ❧

12 K

Puzzle #1, diff. 166, soln. p. 237

2 N3 2

8 N 2 4 1 7 3

N 1 2 6 5

8 4 1 22 5 8 6 4

7 N 2 5 8 6 38 73 4


8 5 2 3 N 6

3 16 2

5 6 4 7 8 1 2

7 61 4 8 3

1 8 5 35 3

5 1 7 6

K 13


2 52 3 8 5

5 8 4 N8 3 6 5 7 N

4 2 5 6 1 88 2 7 5

6 8 N 16 7


4 1 5 3 N8 2 N 4 65 3

8 N6 3 1 2

4 85 8

4 8 2 7 37 5 8 2 4

14 K


7 33 N 6 2 1

4 3 1 N7 6 3 8

8 2 4 52 8 5 1

1 5 7 4 2

N 5


2 8 3 5 1 73 2

7 65 7 N

6 2 46 4 7

3 45 38 1 3 5 7 N

K 15


2 6 N 7 53 2

N 7 54 6 1

3 N7 5 4

5 7 38 N

4 2 6 5 8


N 6 51 2 4

8 N 4 2 11

8 7 4 17

5 2 N 6 31 5 4

N 3 6

16 K


2 4 11 N 3 4 54 6

5 8 13 7

6 7 5

N 88 1 2 6 71 3 8


4 7 3 1

8 4 5 21

1 N 83 2 8 6

5 1 44

3 2 N 55 7 8 3

K 17


N 83 5

N 4 6 87 2 8 6

4 38 N 4 6 5 7

6 1 22 1

5 8 7


4 2

4 2 6 N

N 3 2 6

7 1 2 8

8 7 3 25 6 8 7

7 3 5 21 4

18 K


2 3 13 2 5 47 1 2 8

36 8 3 2

N3 6 1 8

5 N 7 34 5 2


3 N 8 22 4

7 2 6

4 8 25 6 3 N

17 8 2 4

N 3 53 1

K 19


3 5 6

7 45 2 8 1

48 5 N 1 7 4

86 2 8 74 1

3 2 N


1 6 N3 54 3 8

6 4 7 25 1 8

5

8 5 4 6 N 16 8

4 3

20 K


4 N3 7

7 1 4 34 1 6 5

5 2

3 1 4 N1 8 4 7

2 66 4


8 5 N 26 1 7

6 21 5 3

6 16 8 4

3 73 2 14 7 8 5

K 21


N 5 2 13 2 6

4 3 55 N

1 6

8 17 2 3

7 N 82 3 1 5


6 3 54 N

5 8 16 53 5 2 7 41 3

7 3 1

8 55 N 4

22 K


4 N 7 86 4 353 6 7

7 16 1 N

48 5 2

4 N 2 8


3 71 6

N 7 8 2

4 1 2 3

2 8 5 1

N 7 6 42 8

1 5

K 23


5 4 1

8 71 2 3

1

N 1 2 5 8 76 4 5

4 5

8 7 N3


6 13 6 2 8

2 8 35 6 8 3

7 48 4 7 5

8 2 N7 6 5 1

3 7

24 K


N 2 5 6 73 4

1 6 N35 6 2 8

66 2 4

5 74 7 8 1 3


8 6 72 6

6 1 48 1 N 4 7

3 7 54 1

7 1 88 3

3 6 7 4 2

K 25


6 7 35 6 2

N 87 4 N6 7 2 4

1 5 61 8

2 1 78 3 6


N 1 34 21 5 6 2

4 N 11 8 6

7 6 43 8 5 77 86 3 1

26 K


N 8 35 1

48 1 5

2 1 47 6 4

5 6 2

7 12 3 8


1 6 2 81 57 5 43 2 66 1

4 2 57 1 3

8 22 6 1 4

K 27


6 56 7 5 2 3

1 6

7 4 1 52 4

8 7 6 N4 8

N 8 3 5 15 1


3 6

4 52 8 3 4

7 3 6 2

3 1

N 1 8 55 N 8 7

1 66 8

28 K


5 6

N 7 6 21 3 7

5 7 4 11 3 5

45 2 6

81 7 6 5


7 5 2 46 N

1 4 5 83 N

6 2 1 85 7

6 8 N 5

N 84 3 6 7

K 29


3 6 74 3 N 7 25 12 6 N 4

43 6 44 3 2 55 2

6 8


N 82

5 1 2 33 11 4 2 5 3 6

6 1

N 3 7 2

36 8

30 K


8 1 74 6 7

1 2 32 33 1 4 8

8 65 N 4

6 N 2

4 3 6


N 3 5 6 21 5 2 43 8

2 37 1

6 5

8 16 4 1 N

3 5 7 4 6

K 31


N 2 35 N

1 8 71 46 4 8 3

5 2

8 4 2

4 53 1 4


8 6 42 6

2 8 38 3 5

7 1 5 4 N4 2 N

4 7 53 7

6 5 3

32 K


7 86 4

5 4 3 N3 6 4 8

7 12 7 5 3

2 6 7 N1 6

1 5


6 2 51

3 7 6 2 1

N 44 3 7 1

8 53 7 6 1 4

72 5 N

K 33


7 4 N5 7 86 3

4 2 51 3 6 85 1 4 7

2 37 2 4

4


1 61 3 5

6 3 43 5 4

2 5 7 6

3 5 6

7 8 48 7 2

N 4

34 K


1 71 4 8

5 8 3 7 48 4 3 2

2 7 1 84 1 6 N 2

2 N 73 5


6 45 3 2 6

7 8 5

8 5 35 4

2 7 13 7 8

4 6 7 55 4

K 35


6 14 1 7 N2 35 7

2 5

8 65 1 8 N8 4 7 2

1 2 4 6


4 N 16 8

1 2 36 1 4

1 7 6

3 6

7 N 1

8 6 N5 7 8

36 K


7 8 2 42 8 5

1 52

7 2 43 N 6

1 6 78 N 4

3 N


3 21 8 2

7 6 84 5 3

8 7 4 34 6 5

6 1 71 2 3

8 4

II. Black King k“I’m impressed by your knights’ tactical cleverness,” said the Black

King to the White King, “but I don’t think much of the way you’ve

deployed them. Instead of arranging them so that none can reach

each other with a knight’s move, I’d deploy my own Black knights

so that all of them can reach each other, or at least, so each of

them can reach at least one other.”

The White King didn’t believe it could be done, so the Black

King made a quick phone call to one of his generals, and soon

nine Black knights arrived. The Black King arranged them in the

Sudoku garden to demonstrate his idea.

1 n 8 2 6 3 7 5 42 3 7 n 4 5 6 1 86 5 4 1 8 7 2 3 n7 2 1 5 3 8 n 4 65 4 6 7 n 2 1 8 3

n 8 3 6 1 4 5 2 73 1 n 8 5 6 4 7 2

4 7 5 3 2 n 8 6 1

8 6 2 4 7 1 3 n 5

As before, every rank, file, and marked 3×3 block contains

each of the digits 1 to 8 exactly once, and one knight; but the

37

38 k

Black knights are arranged so that each is within a knight’s move

of at least one other.

“If you arrange your knights so that they can’t attack each

other,” said the Black King to the White King, “you’re setting them

up for defeat. Enemy soldiers will pick them off one by one and

they won’t be able to support one another. Deploying them my

way allows them to function as a team, and with proper military

discipline, friendly fire shouldn’t be a problem.”

“Interesting approach,” commented the White King. “It seems

that you can’t ever place a knight in a corner of the board under

those rules, because he would have to have a partner in one of the

two cells he can reach. Both those cells are in the same block, so

the other knight can’t be placed in either of them.” “That’s true,”

said the Black King, “but I can certainly place a knight to attack

a corner cell if I want to, and none of the other cells seem to be

forbidden.”

The kings designed some puzzles under the Black King’s rules,

and if you read the instructions in the previous chapter and the

little story above, you should know how to solve them. Fill in the

missing digits and Black knights to obey the rules of Sudoku, with

the added rule that every Black knight must be supported by (that

is, within a knight’s move of) at least one other Black knight. As

before, the puzzles are in order of increasing difficulty and the

solutions are at the back of the book.

❧ k ❧

k 39


8 4 1 6

n 4 3 16 1 4 5 8

n 7 14 8 5 7

1 6 8

n 4 7 8 37 4 3 6

2 7 3 1


n 3 46 5 3 12 3 8 7

n 8 7 12 8

1 5 3 2

8 5 3 77 2 5 n

2 n 7

40 k


8 6 47 2

2 1 8 72 n 8 1

1 76 3 2

n 7 3 6

3 5 8 n1 8 7


n 1

8 2 1 n7 1 2

6 1 53 6 4 7

2 6 56 8 3

7 2 3 6

7 5

k 41


1 n 55 n

2 7 4 82 5 3 4 1

4 2 7 15 6 n 2 4

3 4 5 15 7

1 6 2


5 3 7 82 5

1 2

4 8 n6 1

2 6 12 7

5 n6 n 3 2

42 k


5 2 13 8

n 8 6 7 48 4 6 7

1 56 3 4 13 1 5 6 7

6 37 8 2


2 71 4 5 8

7 3 n 14 8

5 1 6 78 3

3 7 6 8

n 3 2 77 8

k 43


1 2 n6

7 5 8 22 6 3 4 7

84 n 2 8 1

8 6 2 35

5 1 3


2 74 2 1

4 3 5 2

3 4 61 3 n 8 5

5 6 84 n 8 1

7 3 14 6

44 k


1 7 3 43 8 n 6

7 61 6 7 2

8 2 4 31 4

8 7 6 12 5 n 8


6 33 8 78 3 6

8 2 52 4 6 1

1 7 6

7 1 34 8 n

2 5

k 45


4 n 7 6 52 8

1 66 4 78 5

7 3 2

7 83 26 1 8 4 n


7 47 2

5 3 8 6 2 n8 4

2 31 n 3 7 8 5

2 7 8 41 8 5 3 2 6

46 k


7 3 n 85 66 8 7 2

7 2 14 6

7 2 34 1 6 3

8 77 6 2 5


7 6

4 8 2 54

1 8 6 26 n 1 4 5 87 12 1 3 7

6 53 2 7 6

k 47


7 1 2 31 7

8 3 62 8 n

2 6 7 33 6 57 5 22 4

3 2 7 n


2 n 6 37 4

8 55 4 3 2

7 8

6 n8 2 3 77 3 4 2 1

48 k


1 7 5 n5 2

4 3 7

n 76 8 5 7

1 42 8 3

5 n

n 8 7 2


6 48 3 7 1

5 6

8 1 7 4 2 37 8

1 83 6

5 7 8 4

n 2

k 49


5

n 2 6 7 5 13 8 7

4 1 3 6

7 8 5 n8 n 6

4 1 8 5 6 2

8


1 3 n 5 46 2

n 1

8 6 73 1

6 8 73 2

2 44 n 3 8 5

50 k


1 6 7 4

n 6 2

8 7 65 34 6 2 1

2 6 1 n4 1 7

8 3


4 1

n 8 7 21 2 6 87 3

2 86 1

3 2

7 1 81 7 3

k 51


8 6 7 34

3 7 4 1

n 1 8 44 5

2 3 1 n5 2 6 7

2

8 n 7 2


6 74 5 2

7 8 n 11 4 8

7 36 2 1

6 2 4 34 1 2

n 8

52 k


4 3 2 n 87 1 4 5

n 5 2 1 6 8

6 1 7 4 3 2

4 5 3 76 n 7 8 5


7 88 5 3 6 2

1 8

n 3 83 2

1 2 77 65 4 2 n 3

6 7

k 53


4

n 2 57 6 8

5 66 3 5 8 2 1

1 38 6 5

4 7 35


5 1 8 77 n 5

3 8 5 76

7 14

3 5 2 6

4 1 38 6 5 4

54 k


8 n 2 1

81 8 6

7 5 3 46 5

2 3 4 15 7 n4

2 5 1 8


6 7 4 11 2 3 6

n 3 6 85 7

1 3 5

8 2 5 7 1 n

5 1 2

3 4 n

k 55


1 2

7 n5 8 1

4 1 3

n 2 6 33 7 5

65 3

3 7 n 4 1


8 4 32 1 5 45 6

6 1 n7 1

3 5 81 8

8 2 3 n2 8 3

56 k


n 1 53

7 2 8 6

3 12 3 7 65 6

3 8 2 11

4 5 3


8 12 6 3 8

47 6 53 7 2

2 4 n 1 75

2 3 51 6

k 57


2 8 1 65 2

5 6

3 8 6 48

7 6 4 32 3

3 41 3 7 n


3 5 22 3 6 1

6 5 7

2 1 5

n 3 72 3 4

2 1 8 51 6

58 k


6 44 1 7

8 2

7 8 5 17 2 4

1 4 n 51 3

5 6 n4 3


2 7 34 6 3 2 7 n

6 25 4 7

n 6

4 54 7 3

3 1 65 4

k 59


8 22 3 4

4 5 7 2

8 5 66 4 7 n

7 8 37 1 5 8

8 n 22 7


1 n 4 6

5 4 2 8 n1 36 5

7 6

3 4 5 7 1 85 n

8

60 k


8 16 4 3

1 n 74 n 6

8 5 2

4 2 31 8 3 7

7 6 5


3 2 6 4 78 n 1

8 46 5

11 7

4 2

7 2 42 6 3 7 8

k 61


5 1 6

4 72

3 8 6

4 2

8 2 45 2 1

2 7 61 4 n


3 65 1 7 n

1 3 42 1

3 74 6 3

3 54 6 5 1

1 6

62 k


48 2 6 7 37 2

8 n 46 7 5

3 5 88 13 5 7 8 n

1


54 8

8 4 36 n 3

1 56 7 n 8

8 2 32 4 7 8

7 1

k 63


6 8 11 3

4 5 7 6

42 3 5 1

26 5 2 n

8 22 3 6


3 1 81 2 7

61 8 6 4

6 2 7 5

8 1 66

2 6

3 n

III. Black Queen qA short time later, the kings had dinner together at the Black

King’s palace. The Black King had a Sudoku garden, too—that

is to say, he had one, but the Black Queen had other ideas. She

had been reading about the Eastern practice of feng shui, and she

had the Royal gardeners change all the hedges in the Sudoku gar-

den to optimize the energy flow. In fact, she was still re-arranging

hedges even as the kings were playing with their soldiers, so ev-

ery time they deployed their knights, they did it on a differently-

configured garden.

2 3 7 8 4 6 1 5 n3 2 6 1 5 4 n 7 81 7 8 4 n 5 2 6 36 n 4 5 1 3 8 2 78 6 5 n 3 1 7 4 25 4 n 2 8 7 6 3 1

n 1 3 7 6 2 5 8 47 5 1 3 2 8 4 n 6

4 8 2 6 7 n 3 1 5

The garden is still marked off into nine blocks of nine squares

each, but they are no longer perfect 3×3 squares; instead they’re

apparently random shapes, and different from one problem to the

65

66 q

next. The garden still contains each of the digits 1 to 8, and a

knight, in every rank, file, and block.

There are two kinds of puzzles in this chapter: puzzles with

Black knights, who must each be within a knight’s move of at least

one other Black knight, and puzzles with White knights, none of

whom may be within a knight’s move of any other. All the knights

in any particular puzzle are the same type. If you can’t find one

as a given, you’ll have to figure out by logic which kind to use. A

panel of notable computer scientists has declared that frightening

as they may appear, odd-shaped regions actually make the puzzles

easier by reducing the symmetry that leads to alternate solutions.

See if you agree.

❧ q ❧

q 67


7 5 31 7

5 n 81 n 7

3 72 7 8

8 4 34 8

8 4 n


5 8 2 3 N 72

5

N 4 7 66 7

N 1 8 76

75 7 6 4 2 N

68 q


4 2 8 5 7

N1

1 N1 8 6

5 7

N3

7 8 N 1 3


8 71 2

3 44 62 1 7 3 4 n7 3

n 55 7

4 2

q 69


5 8 4 61 8 5

3 2

7 37 1

5 78 55 3 1

1 3 8 5


3 2 6

45 1

5 4 2

n 13 5 n8 n

51 3 4

70 q


6 5 1 4 7 31 7

41 5 48 3 5 1

2 3 53

2 66 2 1 3 5 4


6 2

8 2 1 56

3 1 8 2

7 1 n 2

33 2 4 8

2 6

q 71


8 4 51 6

5 7 6 2 16

6 8 2

N2 8 7 1 51 36 N 7


1 26 n 8 7

8 47 1 3

6 n7 2 n

1 6 87 6 8

72 q


N 5 8 43 N

3 17 4 3

5 4 36 4

4 6

3 7 N 2


5 1 7 6 8

8 6

8 36 8

3 1

N 5

N 4 3 2 6

q 73


5 8 77 6

6

N 7 84 1 86 N 2

42 1

6 1 N


6 5 7

N 4 216 3

83 8

N2 5 11 N 6

74 q


8 5 N2 N 6

7 6 45 N

8 7 47 3 2

4 26 7


5 84 1 6 8

N 5 4 72 6 4

4 26 4 N

N4

q 75


7 6 3 2

3 7 56 8 7

6 N1 3

14 2 N

5


8 1 3 n 7 6

4 6 n4 2

4

25 6

4 2 88 6 3 4 2 1

76 q


2 4 1

n 76 n

62 5 1 8

35 1

6 83 n 4


4 8 5

8 5 14

5 6

7 N1 2

55 N 3

N 5 7

q 77


3 8 7 N5 N

4 8 5

8 5 N

N 1

N 5 2 3


6 3 5 41 N

7 6 2 N

1 N 4 74 5

4 6 1 N

78 q


2 7 8 N 44 2

1 6

8

13 4

3 54 5 N 3 6


7 5 N7 5

4 32

2 8 1 4 N8

2 75 1

2 N 4

q 79


7 1 5 6 88 1 7

1 n 4 3 7 61 4

4

6 48 n

1


6 41 8

1 7 62 3

N3 2 8

2

8 21 2

80 q


3 1 5 6

4

n 8 34 3 5

5 45 2 8

8 4 78

8 6 4 7


6 5 2 N1 4

15 7

3 N2 1

45 17 4 N 5

q 81


6 5 4

N 3 2

77 2

2 N 77 5

2

41


7 8 5 4 15

3 2 N7 8

77

66

6

82 q


2 43 2 5 8

7 25

56 n

8 3 1 53 n


6 1 85 n

43 1 5

2 75 1 4

57 5

7 n 4

q 83


5 3 1 2

3 n 2

2 1 3 48 7

3 7 6 8

7 8 6

8 6 4 7


4 5 1 3 6

n 2

n 2

42

7 87 3 5

25 7

84 q


6 8 n

7 5 2 41 2

6 14 3

3 7 1 2

5 2 7


6 2 4 1 7 N5 N

5 21 4

3 8 4 5 N

6 4

q 85


1 5 3 47 34 8

86 8

88 n

2 6

8 1 4 n


7 4 6

3 8

n 71

6 7 45

4 37 6

6 n 4

86 q


4 7 5 66 4

1 2 42 1 4

7 2 84 8 7

2 4 78 7

1 4 8 2


5 3 n6

7 6 35 6

2 6

7 6 54

8 7 1

q 87


54 7

3 88 4

2 N1 4

3 82 5

5


3 n 26 4 5

6 2 56 1 4

1 3 6

7 2 n1 n 6

88 q


2 7

1 5 N 2 8 33 6

8 N3 86 4


6 34 2

5 2

8

n 53

3 12 7

8 2

q 89


6

8 5 7 21 6 8

7 N 2 4

2 8 41 8 6 N

1


2 1 4 7 8 32 N

42 5

6 N

8

90 q


4 16 3

4 2

n 3

n 57 5

55

2


6 32 n

7 6 3

4 6 7 5

6 4 8

n 61 5

q 91


7

n 3 4 6

74 5

8

n 8 5 2

n


3 84 1

4 6

4 1 2

6 1 78 2

n 14 n

IV. White Queen QIf you’re familiar with chess rules, you may have observed that

it’s possible to place a queen and a knight so that the queen can

reach the knight with a queen’s move, or the knight can reach

the queen with a knight’s move, but not both. Many volumes of

romantic tragedy could no doubt be written about this state of

affairs.

The White King, however, had no patience for affairs. After

returning from an extended campaign in a foreign land and dis-

covering that while he was away the White Queen had become

overly familiar with one of his White knights, he decreed a new

policy: the Queen and knights were not to be left alone where

they could reach each other in either direction. Here is the White

Queen with eight White knights in the Sudoku garden:

1 5 4 3 N 2 8 7 66 7 2 1 8 4 5 3 N8 N 3 5 7 6 4 2 17 6 N 8 1 5 2 4 34 3 5 2 6 N 7 1 82 1 8 7 4 3 N 6 5

N 8 7 6 2 1 3 5 45 4 6 Q 3 7 1 8 2

3 2 1 4 5 8 6 N 7

93

94 Q

As you can see, each rank, file, and marked-off 3×3 block con-

tains the digits 1–8 and either a White knight (of which there are

eight) or the White Queen (there’s only one of her). Furthermore,

the White Queen cannot reach any knight with a chess queen’s

move (horizontal, vertical, or diagonal, for any distance), and no

White knight can reach the Queen, nor any other White knight,

with a knight’s move.

The puzzles in this chapter follow those rules and the hints

and instructions already given; you may want to use the letter

“Q” for the White Queen. The Queen’s location is given in a few

of the more advanced puzzles, but usually that would be too big

a clue and you’re left to figure it out for yourself.

Special bonus puzzle! There are some cells in the Sudoku

garden that the White Queen cannot possibly occupy in any puz-

zle of this type. If you place her in one of those cells, then even

without worrying about the numbers, you will be unable to find

places for all the knights (with one chess piece in every row, col-

umn, and marked 3×3 block) so that the Queen and knights can-

not reach each other. Which are the forbidden cells? The answer

is given on page 264.

❧ Q ❧

Q 95


2 5 6

N 1 4 57 3 2

1 N 73 8

5 4 17 5 N

N 8 7 32 4 6


2 37 3 6 1

N 45 6 33 2 5 N 6

N 1 8

N 31 3 8 7

2 5

96 Q


3 1

N 1 5 46

4 2 N 75 7 4 3 N

1 N 8 62

3 7 8 54 2


8 N 2 1 6

7 81 N

3 1 44 7

4 6 35 1

1 2

N 6 7 8 4

Q 97


1 4 52 5 3 8 1

N 4 65 N

7 3 66 N

6 5 43 4 1 8 6

4 N 5


3 8 6 51 8

6 N 21 4 2 5 7

N 2

4 33 4 2 6

47 6 3 5

98 Q


2 4 N 74

5 8 N7 3 6

2 1 N 83 6 4 5

3 6

8 2

4 6


6 4 5

N 11 6 N 7

1 7 5 35 78 3 4 2

5 2 1 33 6

N 3 8

Q 99


6 N 44 6 5 8 71 2 57 5 4 3 1

5 4 1 3 74 8 2

N 7 3 1 41 6 2


5 6

N 8 4 17 3

7 2

N 6 1 55 2

8 31 8 5 7

3 4

100 Q


1 57 6 3 N3 8 7 2

6

N 2 6 3 86

2 4 1 7

N 8 4 21 8


3 7 1

8 2 37 3 8 6 4

8 N 44 2 8 N

3 5 22 4 N 8 3

1 4 N1 7 2

Q 101


26 3 4

84 N 2 3 5

2 83 1

4 55 4 N 8 2

2 7 N


6 2 N 11 8 66 8 1

3 1

N 8 2 77 3

5 7 N3 8 4

2 7 3 N

102 Q


N 4 3 6 1 2

8 2 45 3

7 51 6

2 N3 2

4 7 61 5 4 2 8 7


2 8 54 2

5 3 7 2 65 N 1

N 55 8 3

7 3 6 2 82 6

5 3 N

Q 103


2

N 7 6 8 35 7 N

1 8 44 7

8 7 52 6 7

4 8 N 7 6

N


5 2 47 2

2 N 32 7

8 N 13 N 1 4

7 N 2 61 3 74 3

104 Q


6 5 4 16 N

7 6

N 1 5 45 8 N 22 4 8 7

3 21 5

6 1 3 4


2 N 1 5 31 3 8 N

17 3

4 5 2 13 N

83 2 4 77 6 2 1 4

Q 105


7 2 37

N 1 4 56 1 5

8 31 7 N

2 3 47 61 8 N


4 82 8

N 7 6 5

8 6 11 7 2

7 3 N3 4 1 6

N 6

N 1

106 Q


3 7 16

5 7 6 83 8

7 2 1 42 N

3 5

N 6 1 3 7


1 4 N5 1 2

6 8 73 N 1

N 52 1 7 6

87 2

1 2 5 N

Q 107


5 6 1 N 45 7

4 3 86 2

N 2 5 33 1 5 2 7

8 N 2 16 4


N 2 43 5 6 8 N

1 87 3

6 1 4 51 6

2 51 6 7 3 8

4 8 1

108 Q


1 5 87 3 2 5

41 2

N 8 4 3 2

3 7 6

3 8 51 6

N


7 4 3 6

7 1 N3 2

8 4 51 7 8

2 6 N2 7

1 3 48 1 6 N

Q 109


2 72

7 4 6 83 1 7 N 2 6

4

N 7 8 2 5 36 1 4 2

75 4


N 13 4

5 8 61 5 7 8

N 17 2

8 42 N 7

2 5 1

110 Q


1 7 5

N 3 45 2 N

8 1 52

85 7 1

N 7 61 6 8


8 1 21 4 N 3

N 65 6 47 5

8 7 16 8

N 6 7 2 4

Q 111


4 11 N 5 3 6

2

36 7

8 1 7 2 42 5 4 8

N 4 1 2

8 1 2


2 8 37 8 3 4 5

6 4 7 88 N

7 56 3

3 8 1 71 7 6 5 2

N 5 6

112 Q


1 N3 6 8 7

8 21 3 6

1 4 65 7

7 N 2 3 81 8 3


2 N4 6 1 2

7 4 62 8

6 3 5 2 8 44 3

2 3 11 8 2 4

3 8

Q 113


3 42

8 5 4 2 6 76 3 2

2 7 47 6 3

4 N 3 8 7 17

8 N


6 7 4 N 3

N 85 4 7

1 42 7 5

1 87 8

2 6 N4 N 5

114 Q


N 1 44 5

4 1 32 Q

1 4 8 6

3 81 7 8

4 26 3 5


1 2 3 84 78 3 N5 7 3 2

N 12 4

3 6

3 74 2 8

Q 115


7 3 55 1

5 1 6 4

N 54 7 6

6 8

N 7 2 12 8

3 6 N


1 22 5 7 1 3

5 26 52 1 7 N

N 44 1

4 3 2 6 N8 4

116 Q


3 25 1 3 72 N 8

4 65 8 41 3

5 2 6

78 N 1


8 2 17 N

N 3 81 2

5 8 14 7 3

3 42 4 8 5 N

Q 117


4 5 78 Q

1 86 2

3 6 57 15 2 3

3 5 1 N4


N 55 6 3 7

8 6

4 N3 8 5 4 2

5 13 2

6 3 2 17 3

118 Q


7 6 54 2 6

7 33 8 5

6 12 1 3

8 6

7 N 52 5 3


2 N8 3 1 7 N

35 6 4 3 1

3 N

N 1

N 5

8 4 3 61 5 8 4

Q 119


2 7 4

N 1 6

4 3 57 2

5 74 1

6 86 N

4 7 1


1 3 47 1 N

3 82 5 8 1 71

N 3 2

4 26 7 3

V. White Amazon Q

Legend has it that somewhere in Africa there may be tribes of

Amazons: warrior women led by queens who fight like knights.

Accordingly, a fairy chess Amazon can move like a queen or a

knight: any distance horizontally, vertically, or diagonally, or by

an L-shaped knight move. Here’s a diagram of a White Amazon

queen and all the squares she can move to. Note that her chess

symbol is a regular queen’s symbol turned sideways.

• • •

• • •

• • • • •

• • • • •

• • • • Q • • • •

• • • • •

• • • • •

• • •

• • •

You should also take note of the diagonal lines in the diagram.

In Amazonia, they build the Sudoku gardens a little differently

from the ones we’ve seen at the Black and White Kings’ palaces;

as well as having each number exactly once in every row, column,

121

122 Q

and marked 3×3 block, Amazonian diagonal Sudoku requires that

each number occur once along each of the marked diagonals.

Can you place nine Amazon queens in the Sudoku garden so

that they do not attack each other? The White Amazon Queen

couldn’t. She invited eight colleagues for a friendly tea party, and

hoping to minimize friction among monarchs who really didn’t

like each other very much, she decided to arrange the seats so

that no two of the nine Amazons (including herself) could attack

each other by an Amazon’s move—horizontal, vertical, diagonal,

or a chess knight’s jump. She spent hours re-arranging the tea

tables trying to achieve the perfect seating plan; the tea got cold;

harsh words were exchanged, which quickly escalated to arrows

tipped with Greek Fire; and what was meant to be a quiet tea

party turned into a massacre.

The puzzle she faced was actually a variation of an old chest-

nut called the “N -Queens Problem” with which we torture under-

graduates in introductory AI courses. The challenge there is to

place N chess queens (for instance, N might be equal to eight) on

an N ×N chessboard so that none of them can attack each other.

With a standard 8×8 chessboard, there are 92 ways to do it, or 12,

depending on whether you count rotations and reflections as sep-

arate solutions. Making a list of them by hand takes long enough

that you don’t want to do it, but it’s easy for a computer, and that’s

part of why it makes a good teaching problem.

My cleverer students sometimes go on to solve the same prob-

lem using Amazons instead. Then it’s harder, because each Ama-

zon takes up more space than a regular queen, but you can still do

it if you use a 10×10 board or larger. The White Amazon Queen

is out of luck if she wants to invite eight other Amazons to a tea

party on the 9×9 board; there just isn’t enough space.

After consulting her advisors, she determined that for the next

tea party, she would only invite regular queens. Then the seating

arrangements would be easier, and being the only participant with

combat skills would also put her at an advantage should things

turn ugly after all. Here she is in the Sudoku garden with her

guests:

Q 123

6 4 Q 8 3 2 1 7 55 7 3 1 6 Q 8 4 2

8 2 1 4 5 7 3 Q 6

7 8 6 3 Q 1 5 2 41 Q 4 5 2 6 7 8 32 3 5 7 8 4 6 1 Q4 5 8 2 7 3 Q 6 13 6 2 Q 1 8 4 5 7

Q 1 7 6 4 5 2 3 8

As you can see, the garden contains one White Amazon and

eight White queens, with none of them attacking each other; and

just as in the other chapters, each row, column, and marked-off

block contains the digits 1 to 8 as well as one of the chess pieces.

Take particular note of the two marked diagonals. Because this

is an Amazonian Sudoku garden, the diagonals must also contain

each digit once and one chess piece. The puzzles in this chapter

all follow those rules and the same general rules as in the other

chapters. You might want to use the letter “A” for the Amazon.

❧ Q ❧

124 Q


Q 78 2

4 2

83 5 Q

76 7

Q 1 2 5


44 5 7 17 6 3

4 8

1 7 6

Q 2 8 4

Q

Q 125


5 14 6

5 2 Q

Q 1 6

3 46 3

45 8 2


5 3 61 Q

Q 75

7 2

84 33 6

7 Q 5

126 Q


Q2 Q 4

Q 4 51 5

22 3

2 6 81 5 33


Q 57 3

43 2

5 2 Q8

1 6 44 8

Q 4 2

Q 127


Q 5 8 32 4 6

3 52 6

5 Q6 8

4 87 6 1

1 Q 6 4


Q 6 2 41

85 2 4

4 8 55

6

7 4 Q 2

128 Q


8 2 Q1 2 6 3

1 26 3 1 2 4 72 1

8 5 4 2

4 Q 3


3 Q2 4

2 4 Q 66 4

3 7

Q 8 7 11 2

8 Q

Q 129


5 Q5

1 22 3

5 Q4 2

7 57 Q 2

3 8 7


2 Q7 Q 3 2

6 4 Q7

65 8 3

8 6 1 55 3

130 Q


6 1 3 Q

Q 2 4 38

1 5 6

45 Q

2 Q

Q 8 5


Q 2

Q 2

43 8 74 7 6 1

1 2 6

48 5

Q 8

Q 131


Q

1 2 8 5

87 2 3

1 2 76

2 Q

Q 3


8

Q 6

4 5 2 Q

Q 61 7

4 Q6 7 2 82 1

3

132 Q


2

88 4 2

7 34 7

Q 7 2 3 1 55 Q 3

6 Q


8 5 7 46

86 2 5

1 37 8 4

Q

Q6 3 8 Q

Q 133


6 Q6 Q 7

3 4 82

1 Q8

4 7 85 Q 8

1 2


3 1 Q3

1 73 1 5

6 8 Q 25 3 2

3 2

73 4 Q

134 Q


8 47

3 2 45 6

5 2

Q 46 4 Q

87 2


3 7 55 Q

Q 3 6

7 Q3

Q 88 4 1

1 62 6 7

Q 135


3 5 6

8 3

8 5

Q 7 3 6 1 84 7

6 21 3 5


5 1 2 4

Q2

5 Q6 7 2

61 3 Q

Q

Q 6 1

136 Q


6 7 Q1 6 8

1 44 2

Q 71 8 7

8 1

3 6


7 Q 42 7 6 Q

5 12 3

56

7 6 8 Q5 Q 8

Q 137


2 Q5 6

53

26

8 1 41 Q4 3


2 5 8 3 74 2

8

Q7 8 1

51

Q 73 7 8 6 Q

138 Q


Q 54 Q

5 6 121 8 6 Q

7 57 8 2

8


Q 7 4 34 8 1

3 44 1

1 6

7 5 36 2 Q 8

Q 139


Q 8 16 Q

2 75 4

6 4 7 57 6

Q 1

Q 33 6 Q


Q 72 3 Q

8 22 6

Q 48 1

1 4

Q 7 44 3

140 Q


1 7 8 6

Q

2 6

7 1 81 8

35 3 7 Q


Q 1 2

8

6 75 7 4 2 Q

2 61 3

3 4

Q 141


1 Q 2 7 6

8 45

48 Q

88

Q 14 8 Q 3 7


3 Q

2 835 8

5 86 1

7 51 6 4

142 Q


Q 57 2 5

51

Q 5 1 6

36

1 7 38 6


4 Q2 5 6 1

72 8

8 36 2

5

Q 8 6 45 1

Q 143


Q 38 1

6 12 8

Q8 2

36 2 5 47 4


2 Q 6 4 15

4 38

11 2

87 2 3 6 Q

144 Q


7 Q 5

5 76 2

3 8 48 53 7

6 1 Q


6 71 5 2

3 7 8 Q

5 3 6

Q 1 36 7

Q 145


5 26 7 Q7 8

43 5

61

35 Q


3 6 5

8 2 74 76

1

8 15

2

Q 4 6

146 Q


5 Q 1 2

4 7 5

7 55 1 8

1 26

6 Q


Q 57 8

8 1 26 1

2 57

2 76 3

Q 147


3 4 8 55 2

6

41 5 2

6

8

Q 87 5 Q 2


Q 3

Q 4 57

1 3 53 2

6 3 1

Q 12 Q

148 Q


Q7 2

8 37 5

45 2 4

48 6 Q3


2 43 4 6

1 2

1 7 8 Q

1 21 7 3

Q 3

VI. Black Amazon q

In the Black Amazon Empire, there are many queens, and each

one has one or more Black kings captured in wars with neigh-

bouring tribes. The queens are constantly hoping to add to their

harems, while guarding their existing husbands against capture,

so arranging them in the garden to avoid bloodshed and hanky-

panky can be a difficult problem. Here’s an example:

3 4 7 6 2 5 q 8 1

k 2 1 8 7 4 3 5 65 6 8 k 3 1 4 7 26 3 4 1 5 2 8 q 71 8 2 4 k 7 5 6 37 k 5 3 8 6 2 1 44 5 6 2 1 q 7 3 82 7 3 5 6 8 1 4 q

8 1 k 7 4 3 6 2 5

Every Black Amazon is within an Amazon’s move of at least

one Black king. Furthermore, every king is within an Amazon’s

move of exactly one Black Amazon, and no two Amazons can at-

tack each other. Although you will seldom see it, kings are al-

lowed to be within a king’s move of each other. There are also the

149

150 q

usual rules that every rank, file, and marked-off 3×3 block con-

tains the digits 1 to 8 once each as well as exactly one of the chess

pieces, either a king or an Amazon; and since this is an Amazo-

nian Sudoku garden, the same rule applies along the two marked

diagonals as well.

This is the occasion I told you to save your “K”s for; you’ll

want them for the kings, and probably an “A” for the Amazons,

to solve the puzzles in this chapter. By now you should be quite

familiar with the other rules. The difficulty ratings in this chapter

are some of the highest in the book, but that is partly because they

are based on a computer analysis and the computer seems to have

special difficulty with the Black Amazon rule variation. Some of

the decisions made in solving these puzzles involve a large num-

ber of alternatives, which is the worst case for the computer solver.

Humans are expected to be able to narrow down such decisions

by throwing out the obviously incorrect possibilities, so a human

should find these puzzles easier than the computer does.

❧ q ❧

q 151


2 4 k 5

q

k 6 2

7 1 41 7 5 3 8 k

k 6 45 6 8

2

8 3 4 1


7 4 1 k 66 4

6

q 7 11 55 2 8

q

4 k

k 2 8 4 3

152 q


1 8 k2 3 1

5 44 8 k

5 1

8 3 k6 8

7 6 83 k 7


6 5 3 7

q 62 1 k 6

7 6

3 k1 8 4 3

2 7

k 7 6 2

q 153


57 66 2 4 8

4 8 2 q

2 6

k 7 3 57 3 8 k

2 57


83 7 1

q 26 7 3

5

8 4 6

k 1

q 2 36

154 q


6 kq 6

3 8 6

86 4 1 2

15 3 1

5 q8 3


2 71 k 3 7 8 5 48 k

2 6

5 7

q 2 6 4 7 8 53 4

q 155


3 8 7 5q 5

1 32 8

3 1 5 65 q

7 54 8

4 k 8 1


3 4 6 2

4 7 k

q 16 4

k 54 1

6 33 4 6

1 7 q 4

156 q


5 1

k 6

78 4 7

2 6 4 k

k 3 5q

3 14 8


4 3 86 2 q

6

7 36 8

5 q

k2 8 5

5 6 1

q 157


k 1q 3 7 1 2

4 3 8

8 6 7

3 7 8 q 1

q 6


7 1 3

q 34

4 8 1 k7 5 8 1

k 3 7 51

2 k1 7 8

158 q


6 2q 8 5 1

5 3 42

1 q

6

4 1 8

q 8 4 31 2


86 5 1

6 q 3

q

6 2 7 5 88

2 4 84 8 56

q 159


1 k3 6 7

82 8 5

8 26 4 k

25 1 7

k 6


8

q

6 k 88 5 4 q

1 6

7 2 6 51 7 4

38

160 q


8 6 q

2 8

5 q 2 12 4 7 8

3 7 k 6

6 4

k 5 3


1 q

5 3 47 k

8 47 11 8

6 82 8 6

6 5

q 161


q 43 56 2 5 q

3 1

8 6 4 53

8 7


8

q 8 25 6 k1 66 34 12 q 8

3 1 6

4

162 q


1 8 76 4

q 6

k 2 4 5

4 8 q 13 8

4 k4 5 6


6 4

7 8 12 7 5

k 4 7 15 4 k

k 2 6

5 k

q 163


4 66 3 1 4

7 21 k 8 7

1 22 3 8 4

k 2


54

6 1 3 k

k 6 82 5 1

1 7 q

6 4 8 5

84

164 q


42 q 5 78

43 8 7

q

84 1

2 1 6 k


73 5 2

8 4 q 34

2 1 7 36 1

7 5 6 3 4

q 165


6 43 6

4 q

76 7

5 8 k6 21 q 8

2 q


2 8 k 36 7 8

8 33 1

1 44 q

6 22 4 k

8 5 k 6

166 q


k4

2 4 6

4 6 8 3 5

8 1 2 6 k

q 7 31

5


2 55 4 2 k

17 6 k

6 3 15

6 2 3 8

q 6

q 167


q 51 6

7 2 k5

4 37 6

k 2 1 46 3


7 2

k 8 76

3 5 q

4 6

k 3 46

4 1 k7 2

168 q


8 4 6

7 6

3 87 6 8 2

8 2 6 77 5

4 1 k


6 k 1 57

13 8

88 4

5 q

k 2 73

q 169


8 2 7

5 46

1 62 6 3 q

6 k

q 1 2 7 5 4


7 k 4 5 17 6

5 q 8 7

6 5 1 72 5 4 6

3

170 q


1 k 3 76 4 5 2

56 2

3 5

q 74

k2 1


7 25 1 4

8 78

k 6 1 48

5 62 8 1

7 2

q 171


45 6 2

1 3 22

6 21

8 4 13 k 6

5


4 6 51 3

5 47

8 5 q

3 1 87 6

k

172 q


4 16 7 k

6

4

k 5 4 85

22 6 3

5 2


6 7 1

8

q 72

7 8 3 2

3

k 84

2 k 4

q 173


1 k3 6 2

7 3 5 6

86 2 k

77 3


87 5

6

8 5 65 7

72 q

4 6 71 5

174 q


71 3 5

k 1 6

4 7 q

6 7 41 8 4

6 3 q

6


81 2 7 6

6 48 5

5 37 8

74 k5 1

q 175


2 71 8

2 86 k

5 17 5 6 4

32 7 8


5

q 6 5

8 6

4

k 2

83 16 1 7

1

VII. Pawns PpAt the end of the day, after the kings and queens had gone home,

the Black and White pawns were left to clean up. Being puzzle

fans themselves, they decided to make a game of it.

“Listen, fellows,” said a Black Pawn, “Since even and odd num-

bers appear equally often in the Sudoku garden, let’s use those to

decide who erases which. Black pawns can take the odd numbers,

and White pawns can take the even numbers.”

“That’s fine,” said a White Pawn, “but I’m accustomed to mak-

ing diagonal capture moves while playing chess, and I want to

keep my skills sharp. So let’s all find places in the Sudoku garden

where our captures are the appropriate kind of number, either

even or odd.” Here’s an example of what he meant:

p3 7

2 4

P

177

178 Pp

Pawns capture by moving one space diagonally forward. We

are assuming that the Sudoku garden is drawn like a standard

chess diagram, so that the direction of movement is up in the

diagram for White pawns and down for Black pawns.

“That’s fine as far as it goes,” said the Black Pawn, “but there

are a lot of subtleties to our job in a chess game. For instance,

what about promotion and en passant captures?”

“Let’s try to keep it simple,” said the White Pawn. “We won’t

worry about en passant capturing, and if we say that every pawn

has to be able to capture two numbers of the appropriate type,

that also eliminates promotion. If I were in the top rank, for

instance, my capture moves would be off the board, and so it

wouldn’t matter that by that point I might have changed into an-

other piece. That means any pawn in the top rank has to be a

Black one, and any pawn in the bottom rank has to be White. It

also means that none of us can be on another’s capture square,

since that would leave the other with less than two numbers to

capture.” Here is an example:

2 6 3 5 8 7 1 p 45 4 1 2 6 p 3 8 77 8 P 1 3 4 5 6 2

3 2 6 7 5 1 P 4 8

P 1 7 3 4 8 2 5 6

8 5 4 p 2 6 7 3 16 P 5 4 1 2 8 7 31 7 8 6 P 3 4 2 54 3 2 8 7 5 6 1 P

Pp 179

Every rank, file, and marked 3×3 block contains each of the

digits 1–8 once, and one pawn, either Black or White. White

pawns are positioned to capture two even digits each, and Black

pawns to capture two odd digits each. The pawns did have to

make an exception for the two files at the sides of the board:

pawns on the the extreme left and right can each capture only

one digit of the appropriate type.

The puzzles in this chapter should be quite straightforward

after the others you’ve done, and they’re on the easy side, too.

You’re on your own to find an appropriate way of recording the

difference between Black and White pawns.

❧ Pp ❧

180 Pp


4 8 p

P 4 7 3 55 3 P

1 7 p7 6 1 44 p 6

5 8 45 P 8 4 1

2 4 5


8 7 4 36 8

2 52 p 1 7 5 6 4

8 4 3 p 6 5 78 p

P 55 6 7 8

Pp 181


43 7 6 p

P 4 3 56 P 1 7 8

52 8 6 7 3

8 1 4 66 3 8 2

4


5 4 6

4 3 6 P7 1

7 P 3 26 P

p 3 8 57 1

4 7 3 p8 2 6

182 Pp


2 5 88 4 32 4 8 p

8 1 35 7

1 6 p8 2 1 p

6 3 14 1 7


4 6 38 4 7 1

2 85 8 6 3

1 84 p 5 1

P 88 7 2 P1 2 4

Pp 183


5 81 P 5

3 4 P 5

p 47 2 3 4 1 8

p 36 4 2 1

5 6 84 6


7 3 65 4 3 1 p3 4 8

82 p 6 5

2

P 6 45 8 1 6 P

8 P 2

184 Pp


4 8

2 31 7 p

7 3 p 6 42 8

7 1 5 p3 P 6 5 76 3 4


8 2 6 5 P

P 43 5 4 2

8 7 6 p2 P 7 1

5 22 6 8 p 1

Pp 185


7 p 8

p 1 4 5

P 35 3

3 2 5

p 13 2

P 2 8 11 4 3


4 11 3 8 7

4 5 2

4 P5 P

p 6

3 4 p

p 2 7 46 5

186 Pp


5 6

7 26 7 4 P 1

8 2 7

4 5 38 6 4 P 3

5 81 P


6 7 1 52 4 8

1 4 7

p

p 65

4 2 8

P 1 35 2 1 6

Pp 187


3 8 4

P 7 3 15 6 3 2

p4 1 8 P

2 1 4 p

8 7 1


8 p3 5 2

6 1 5 2 35

2 4 87 6

P1 p 5

6 2

188 Pp


3 56 73 1 55 8 4

17 1 p8 5 71 2

8 4


8 5 13 8 6

44 P 2

5 6

7 48 P 3

7 1 52

Pp 189


1 35 7 8 P

7

P 7 8 15 2

6 5 1 p5

6 1 4 38 1


5 4 1

P8 1 7 6

5 84 2 p

1 p4 2 8 p

26 P 7

190 Pp


8 4 61 6 2 p

p 16

5 8 6 32

7 61 3 7 8

6 1 P


1

8 7 2 P2

6 7 1 3

P 4 75 6 1 8

3

p 5 6 2

8

Pp 191


7 4

P 4 3 7 56 7 P 3 5

2 41 7 3 6 8

p 5 6 3 1

4 7


2 4 36 P 5

7 54 2 5

7 46 p 8

p 48 7 P

7 1 8

192 Pp


8 62 43 p 5

2

3 P 6 2 8

p

p 4 11 5

1 3


6

p 7 3 13 1 p

1 2 38 5 7 2

2 4 62 1 P

1 P 8 52

Pp 193


1 7 36 2 p

p 7 14 8

P 1

P 6

3 2 46 8 P4 6 2


6

4 8

P 6 7 3

P 7 4 21

6 5 7 35 4 7 1

3 21

194 Pp


41 3 p

p 8 57 21 8 P 7 4

5 3

P 5 2

3 1 41


3 8 72 p 4

P 5

P 6

77 86 1

4 1 6

8 P 7

Pp 195


p 3 41 P

8 3

P 5 77 1

8 2 4

p 21 5

4 6 2


4 7 1 p4 8

26 7 P 5

3 5

p 2 1 7

P4 2

6 8 7 2

196 Pp


p 76 2 3 p

P 8 4 35 8 P 6 4

4 5 6 2

3 4 8 77 4


6 1 83 6

4 1 6 2 7 5

P2 1

47 8 4 6 P 3

4 7

P 7 2

Pp 197


5 66 7 4

P8 2 4

3 72 1 3

p4

4 2 P 3 5


55 3 8 6 p 71 4 5

6 P 2 53 5 1 P

4 2 6 3

6 3 1 2

198 Pp


3 2 p 8 6

4 2 8 p4 7

8 41 3

1 4 5 26 1 4 5 p


5 4 3 p 2

P2 8

3 16 2

6 14 7 p7 6

8 5 6

Pp 199


7 6

4 2 13 5 6

1 48 P

4 72 3 75 1 6

1 5


7 1

8 2 6

3 7 56 P 8

2 p 3

p 4 2

7 1 2

8 4 33 5

200 Pp


65 74 6

P 3 8 5

7 6 p 44 3

32 8 5 P


6 5 4 7 12 p

7 8 31

7 P2

5 3 P

p 2

3 1 P 6 2

Pp 201


p 2 11 47 2 5 P

85 4 2 3 8

6

4 1 5 7

p 83 2 6


5

8 3

p 6 2

4 1

P 5 7 6

8

p 1

p7 8 4 5

202 Pp


3 p 2

p1 78 5 1 7 3

15 4 1 6 P

p 53

2 5 1


2 1 6

7 2

87 6 4

8 P 2

4 7 p8

1 p5 7 3

Pp 203


2 7 14 8

1

P 61 P

5 41 3 4 8 6

52 7


6 73 2

3 p2 5

5 8 1 44 6

2 P5 2

1 3

204 Pp


1 46 2 7 1

2 6 4

P 7 85

8 6 14 5 8

6 3 2 13 8


34 7 2 3

5 1 P8 2 1

8 p 66 3 1

P 2 14 2 6 5

8

Solutions

205

206 Solutions

Solution for Puzzle #145:

6 3 4 2 8 1 5 N 78 6 5 7 1 4 N 3 23 N 1 5 2 6 8 7 44 8 7 3 N 5 2 1 65 7 6 N 3 2 1 4 8N 4 8 1 6 7 3 2 57 1 2 8 5 N 4 6 31 2 3 4 7 8 6 5 N2 5 N 6 4 3 7 8 1


3 7 5 k 6 1 2 8 44 2 6 3 8 5 7 1 q

1 8 q 4 2 7 6 5 36 5 4 7 1 8 3 k 22 3 7 6 5 k 8 4 1k 1 8 2 3 4 5 7 65 4 3 8 k 6 1 2 78 q 2 1 7 3 4 6 57 6 1 5 4 2 q 3 8


7 8 6 4 Q 5 1 2 3

Q 4 2 7 3 1 5 6 81 5 3 8 6 2 4 Q 74 3 7 1 5 Q 6 8 22 6 Q 3 8 4 7 1 58 1 5 2 7 6 Q 3 43 Q 1 5 4 8 2 7 66 7 4 Q 2 3 8 5 15 2 8 6 1 7 3 4 Q


6 2 1 4 N 7 8 3 52 7 3 1 5 4 6 8 N8 N 5 7 4 3 2 1 64 3 8 2 6 5 N 7 11 6 7 5 3 8 4 N 25 1 N 8 2 6 7 4 37 5 4 N 1 2 3 6 8N 4 6 3 8 1 5 2 73 8 2 6 7 N 1 5 4


1 2 n 8 3 5 4 7 67 8 3 4 n 6 2 1 55 4 6 7 2 1 3 8 n4 1 5 6 7 8 n 3 2n 6 2 1 4 3 8 5 78 3 7 n 5 2 6 4 13 n 4 5 6 7 1 2 86 5 8 2 1 4 7 n 32 7 1 3 8 n 5 6 4


5 4 8 2 1 N 6 3 71 3 2 6 7 4 N 5 87 N 6 3 8 5 2 4 1N 6 7 8 3 1 5 2 48 2 4 5 N 7 1 6 33 1 5 4 6 2 7 8 N6 7 3 1 2 8 4 N 54 8 1 N 5 6 3 7 22 5 N 7 4 3 8 1 6

Solutions 207


6 2 8 4 1 N 3 7 54 5 Q 2 7 3 6 8 11 3 7 6 5 8 4 2 N7 8 1 3 6 5 2 N 45 4 2 1 N 7 8 3 63 N 6 8 2 4 5 1 72 1 5 7 3 6 N 4 88 6 3 N 4 1 7 5 2N 7 4 5 8 2 1 6 3


Q 6 2 1 3 4 7 5 88 1 7 2 6 5 Q 4 35 3 4 Q 7 8 2 1 61 8 5 3 2 Q 6 7 47 2 6 4 5 1 3 8 Q

4 Q 3 6 8 7 5 2 16 4 1 5 Q 2 8 3 72 7 Q 8 4 3 1 6 53 5 8 7 1 6 4 Q 2


7 1 3 4 6 N 5 2 85 4 8 1 2 7 3 6 N

Q 2 6 3 5 8 7 1 43 6 7 5 4 2 N 8 14 8 1 N 7 6 2 5 32 5 N 8 1 3 4 7 66 N 2 7 3 1 8 4 58 7 5 6 N 4 1 3 21 3 4 2 8 5 6 N 7


2 6 8 k 4 1 3 5 77 q 1 3 5 8 2 4 65 3 4 2 6 7 k 1 83 4 7 1 k 2 8 6 56 1 5 4 8 3 7 2 q8 2 q 6 7 5 4 3 14 7 3 5 1 q 6 8 2k 5 2 8 3 6 1 7 41 8 6 7 2 4 5 k 3


3 7 6 1 4 2 5 8 Q8 N 4 5 7 3 2 1 61 2 5 6 8 N 3 4 74 1 2 7 N 5 6 3 8N 5 3 8 2 6 1 7 46 8 7 3 1 4 N 2 55 4 8 2 6 1 7 N 37 3 1 N 5 8 4 6 22 6 N 4 3 7 8 5 1


7 5 6 8 3 n 4 2 11 n 8 2 6 4 7 5 33 4 2 1 5 7 n 6 8n 8 4 7 1 2 5 3 66 2 7 3 4 5 8 1 n5 3 1 n 8 6 2 7 44 6 3 5 2 8 1 n 78 7 5 6 n 1 3 4 22 1 n 4 7 3 6 8 5

208 Solutions


5 1 2 n 8 7 6 3 44 6 3 2 1 5 7 8 n8 7 n 4 3 6 1 2 52 5 1 8 6 3 4 n 7n 8 6 5 7 4 3 1 23 4 7 1 2 n 8 5 61 n 5 6 4 8 2 7 37 2 4 3 n 1 5 6 86 3 8 7 5 2 n 4 1


4 8 6 k 1 5 2 7 35 q 2 7 6 3 8 4 13 7 1 2 4 8 k 6 56 2 4 3 8 1 7 5 q

1 5 k 4 7 6 3 2 88 3 7 5 k 2 6 1 4

q 1 8 6 2 4 5 3 77 6 5 1 3 k 4 8 22 4 3 8 5 7 1 q 6


5 3 2 6 4 1 n 8 77 4 8 5 n 2 6 3 1n 6 1 8 3 7 4 2 52 7 4 n 6 8 5 1 31 n 3 7 5 4 8 6 26 8 5 2 1 3 7 4 n3 1 n 4 8 5 2 7 68 5 7 1 2 6 3 n 44 2 6 3 7 n 1 5 8


3 7 6 1 4 5 2 k 8

q 5 8 2 6 7 4 3 14 1 2 3 8 q 5 7 62 k 5 7 1 6 8 4 38 6 4 5 k 3 1 2 77 3 1 4 2 8 k 6 55 4 7 k 3 1 6 8 26 2 3 8 5 4 7 1 q

1 8 q 6 7 2 3 5 4


5 3 8 1 2 6 7 k 41 2 4 k 7 3 6 5 8

q 6 7 5 8 4 1 2 37 5 3 4 6 2 k 8 16 8 2 7 k 1 4 3 54 1 q 3 5 8 2 6 72 4 6 8 1 5 3 7 q

3 7 5 6 4 k 8 1 28 q 1 2 3 7 5 4 6


N 1 8 6 3 7 4 5 25 6 2 4 8 1 3 7 N7 3 4 N 5 2 8 1 66 2 N 7 4 3 1 8 53 8 5 1 2 N 7 6 41 4 7 5 6 8 N 2 34 7 3 2 1 6 5 N 88 N 6 3 7 5 2 4 12 5 1 8 N 4 6 3 7

Solutions 209


p 7 5 6 8 2 1 4 34 3 1 7 P 5 2 8 68 6 2 1 3 4 7 P 51 p 4 3 2 8 5 6 77 2 3 P 5 6 4 1 85 8 6 4 7 1 p 3 26 4 8 2 1 7 3 5 p2 1 P 5 6 3 8 7 43 5 7 8 4 P 6 2 1


4 7 1 5 6 N 2 8 36 8 Q 7 3 2 5 1 42 5 3 1 4 8 6 N 71 2 6 8 7 3 4 5 N7 N 8 6 5 4 3 2 15 3 4 2 N 1 8 7 63 6 7 N 8 5 1 4 28 4 2 3 1 7 N 6 5N 1 5 4 2 6 7 3 8


2 8 3 4 k 7 6 1 56 7 1 3 8 5 q 4 25 k 4 6 2 1 7 3 83 5 8 q 7 2 1 6 41 4 7 5 6 3 8 2 k

k 2 6 1 4 8 5 7 34 1 q 2 5 6 3 8 77 3 2 8 1 q 4 5 68 6 5 7 3 4 2 k 1


8 4 3 7 6 1 p 5 25 6 p 4 2 3 7 1 82 1 7 5 8 p 6 3 46 3 4 2 7 8 1 P 57 8 1 3 P 5 2 4 6p 2 5 6 1 4 3 8 73 5 2 1 4 6 8 7 P4 7 8 P 3 2 5 6 11 P 6 8 5 7 4 2 3


6 p 2 5 1 7 4 3 85 3 7 p 8 4 2 6 14 8 1 6 3 2 7 p 52 6 4 3 P 5 1 8 78 7 p 2 6 1 3 5 41 5 3 7 4 8 6 2 p7 2 8 4 5 6 P 1 33 4 5 1 2 p 8 7 6P 1 6 8 7 3 5 4 2


2 N 7 3 8 6 1 5 48 3 5 1 4 2 6 7 N1 6 4 7 Q 5 3 8 2N 5 8 6 7 4 2 3 16 7 1 2 5 3 4 N 84 2 3 N 1 8 5 6 73 4 N 8 6 1 7 2 55 8 2 4 3 7 N 1 67 1 6 5 2 N 8 4 3

210 Solutions


3 N 4 7 1 2 5 8 61 7 8 4 6 5 3 2 N5 6 2 8 N 3 4 7 17 4 3 5 8 N 6 1 28 5 6 3 2 1 N 4 7N 2 1 6 4 7 8 3 52 1 5 N 3 8 7 6 44 8 N 1 7 6 2 5 36 3 7 2 5 4 1 N 8


6 1 5 7 3 2 Q 8 4Q 2 7 8 4 1 6 5 33 4 8 Q 6 5 2 1 74 7 6 1 5 8 3 Q 21 5 3 2 Q 4 7 6 82 8 Q 6 7 3 5 4 15 6 1 3 8 7 4 2 Q8 3 4 5 2 Q 1 7 67 Q 2 4 1 6 8 3 5


1 2 3 8 7 6 4 k 5

q 7 4 3 5 2 8 6 16 5 8 4 1 q 3 2 73 1 k 6 4 8 7 5 22 8 5 1 k 7 6 4 34 6 7 2 3 5 k 1 85 3 1 k 8 4 2 7 68 4 6 7 2 1 5 3 q

7 q 2 5 6 3 1 8 4


1 5 8 2 q 7 6 4 34 6 3 1 5 8 7 2 q

2 7 k 6 4 3 5 1 87 8 6 3 1 4 k 5 2k 2 1 7 8 5 3 6 43 4 5 k 6 2 1 8 78 q 7 5 2 6 4 3 15 1 4 8 3 k 2 7 66 3 2 4 7 1 8 q 5


6 3 2 8 7 N 4 1 54 8 1 5 6 2 N 7 3N 5 7 1 3 4 6 8 21 N 5 3 4 8 2 6 73 2 4 7 Q 6 8 5 17 6 8 2 5 1 3 N 42 7 6 4 8 5 1 3 N8 1 3 N 2 7 5 4 65 4 N 6 1 3 7 2 8


6 N 7 2 4 1 5 8 33 5 8 6 Q 7 1 4 22 1 4 5 3 8 6 7 N1 3 5 4 6 2 7 N 8N 7 2 8 1 3 4 6 58 4 6 7 5 N 2 3 15 8 1 3 7 4 N 2 64 2 N 1 8 6 3 5 77 6 3 N 2 5 8 1 4

Solutions 211


2 7 4 1 8 q 3 5 63 q 5 6 2 4 8 7 16 1 8 7 3 5 4 k 2k 5 3 4 7 1 6 2 84 2 6 k 5 8 7 1 31 8 7 2 6 3 5 4 q7 6 q 3 4 2 1 8 55 3 2 8 1 7 k 6 48 4 1 5 k 6 2 3 7


3 8 6 7 5 1 2 k 4

q 5 2 8 4 6 3 7 11 4 7 3 2 q 6 5 84 6 3 2 7 5 8 1 k5 7 1 6 k 8 4 2 38 2 k 1 3 4 5 6 77 k 8 4 6 2 1 3 56 3 4 5 1 7 k 8 22 1 5 q 8 3 7 4 6


5 7 1 6 2 Q 8 3 44 2 Q 3 8 5 6 1 78 3 6 7 4 1 Q 5 27 Q 8 4 1 2 5 6 31 5 4 Q 3 6 7 2 83 6 2 5 7 8 4 Q 1Q 4 7 2 6 3 1 8 52 8 5 1 Q 4 3 7 66 1 3 8 5 7 2 4 Q


8 4 7 3 6 2 1 5 Q5 6 1 4 N 7 3 8 23 N 2 8 5 1 7 6 47 8 N 6 2 3 4 1 51 5 4 N 7 8 6 2 36 2 3 1 4 5 8 N 7N 7 8 2 1 4 5 3 64 1 6 5 3 N 2 7 82 3 5 7 8 6 N 4 1


7 2 5 6 4 3 8 1 p4 8 1 2 5 P 6 7 33 p 6 8 1 7 2 5 41 6 3 4 2 5 7 P 88 5 2 7 p 6 3 4 1p 4 7 3 8 1 5 2 65 7 p 1 3 8 4 6 22 1 8 5 6 4 P 3 76 3 4 P 7 2 1 8 5


8 p 3 7 4 5 6 2 11 6 7 2 p 8 5 4 35 2 4 3 6 1 P 7 83 8 5 6 2 7 4 1 p6 4 1 8 5 P 2 3 72 7 P 1 3 4 8 5 6p 5 8 4 1 3 7 6 27 3 6 5 8 2 1 p 44 1 2 P 7 6 3 8 5

212 Solutions


3 4 8 2 1 N 5 7 6N 7 6 8 5 4 2 3 12 1 5 3 7 6 8 4 N1 5 7 6 Q 8 3 2 46 N 3 5 4 2 7 1 88 2 4 1 3 7 6 N 55 3 2 4 6 1 N 8 74 8 N 7 2 5 1 6 37 6 1 N 8 3 4 5 2


7 6 3 2 1 8 n 4 58 5 4 3 n 6 2 7 12 1 n 7 4 5 8 3 65 7 2 n 3 4 6 1 8n 3 8 5 6 1 7 2 41 4 6 8 2 7 3 5 n4 n 7 1 8 3 5 6 26 8 5 4 7 2 1 n 33 2 1 6 5 n 4 8 7


6 2 5 p 4 7 8 1 31 4 3 2 5 8 p 7 6P 7 8 3 6 1 2 5 44 p 6 5 8 3 1 2 77 8 1 4 2 6 5 3 P3 5 2 7 1 p 4 6 82 6 4 8 7 5 3 P 18 1 p 6 3 2 7 4 55 3 7 1 P 4 6 8 2


6 Q 5 1 7 2 8 3 42 8 7 3 4 5 Q 1 63 4 1 8 Q 6 2 7 5

Q 2 4 5 8 7 1 6 35 7 8 6 3 1 4 2 Q1 6 3 Q 2 4 5 8 74 3 6 2 1 Q 7 5 87 5 2 4 6 8 3 Q 18 1 Q 7 5 3 6 4 2


7 4 1 N 6 2 8 5 38 6 2 3 5 1 N 4 73 N 5 4 8 7 2 6 16 3 8 1 4 5 7 2 N2 1 4 7 N 3 5 8 6N 5 7 6 2 8 3 1 45 7 3 8 1 4 6 N 24 8 N 2 7 6 1 3 51 2 6 5 3 N 4 7 8


7 8 3 2 6 5 Q 1 46 2 4 Q 8 1 5 7 31 Q 5 3 4 7 2 8 65 7 2 8 Q 6 4 3 14 1 8 7 3 2 6 Q 5Q 3 6 1 5 4 8 2 73 4 Q 6 7 8 1 5 22 5 7 4 1 Q 3 6 88 6 1 5 2 3 7 4 Q

Solutions 213


3 5 4 1 8 p 6 7 28 2 p 7 5 6 3 4 11 7 6 3 2 4 P 8 54 3 8 P 1 5 7 2 6p 6 5 2 7 3 8 1 47 1 2 4 6 8 5 P 36 p 1 5 4 7 2 3 85 4 7 8 3 2 1 6 p2 8 3 6 P 1 4 5 7


3 8 7 1 6 p 2 5 44 p 6 7 5 2 3 1 81 2 5 8 3 4 p 6 78 6 P 2 4 5 1 7 32 7 3 p 1 8 5 4 65 4 1 6 7 3 8 2 P

p 1 4 3 2 6 7 8 57 5 8 4 p 1 6 3 26 3 2 5 8 7 4 P 1


5 Q 2 7 4 8 3 6 18 6 1 3 N 2 7 5 44 3 7 6 1 5 2 N 83 8 N 1 7 6 5 4 22 4 5 N 8 3 1 7 61 7 6 5 2 4 8 3 N

N 5 3 2 6 1 4 8 77 1 8 4 3 N 6 2 56 2 4 8 5 7 N 1 3


1 6 3 8 n 7 4 5 24 8 2 1 5 3 n 7 6n 5 7 6 4 2 3 8 15 1 n 2 3 8 7 6 46 2 4 5 7 1 8 3 n7 3 8 4 6 n 2 1 52 7 6 3 1 4 5 n 83 4 5 n 8 6 1 2 78 n 1 7 2 5 6 4 3


p 8 1 5 4 2 3 6 77 5 4 1 6 3 2 8 p6 3 2 7 8 p 5 1 42 P 7 8 3 6 1 4 55 1 8 4 P 7 6 2 33 4 6 2 5 1 p 7 84 7 P 6 2 5 8 3 11 2 3 p 7 8 4 5 68 6 5 3 1 4 7 P 2


8 6 1 n 7 4 5 3 23 n 2 1 5 8 7 4 64 7 5 6 3 2 1 8 n6 1 3 5 8 n 2 7 47 5 8 2 4 6 3 n 12 4 n 3 1 7 6 5 8n 3 4 7 6 1 8 2 55 8 6 4 2 3 n 1 71 2 7 8 n 5 4 6 3

214 Solutions


5 8 1 6 3 4 2 7 Q3 4 Q 2 5 7 1 6 87 6 2 1 8 Q 3 4 58 7 4 Q 1 2 5 3 6Q 5 3 8 7 6 4 1 21 2 6 5 4 3 8 Q 72 3 8 7 Q 1 6 5 46 1 7 4 2 5 Q 8 34 Q 5 3 6 8 7 2 1


5 2 4 7 1 p 8 6 3P 8 3 6 5 4 7 2 17 6 1 2 8 3 P 4 51 4 6 8 7 2 5 3 p8 5 7 3 p 6 4 1 22 3 p 5 4 1 6 7 84 7 8 1 2 5 3 p 63 P 2 4 6 8 1 5 76 1 5 P 3 7 2 8 4


2 4 1 n 5 6 8 7 35 n 7 8 3 1 4 6 26 8 3 2 7 4 1 5 n

n 7 5 4 6 3 2 1 83 2 4 7 1 8 5 n 61 6 8 5 2 n 7 3 44 3 6 1 8 7 n 2 58 1 2 6 n 5 3 4 77 5 n 3 4 2 6 8 1


5 4 2 3 Q 7 6 8 1N 3 8 6 4 1 7 2 56 7 1 2 5 8 4 N 31 5 7 8 6 2 3 4 N2 N 6 7 3 4 1 5 83 8 4 5 1 N 2 7 68 1 5 4 7 6 N 3 24 2 N 1 8 3 5 6 77 6 3 N 2 5 8 1 4


2 5 Q 8 3 4 7 1 64 6 8 7 1 Q 5 2 33 7 1 6 5 2 4 Q 8Q 1 5 4 6 3 8 7 27 3 2 Q 8 5 6 4 16 8 4 1 2 7 Q 3 51 2 7 5 Q 6 3 8 48 Q 6 3 4 1 2 5 75 4 3 2 7 8 1 6 Q


1 3 p 6 2 7 5 8 48 7 4 3 5 p 2 1 62 6 5 4 1 8 7 p 34 p 8 7 6 2 1 3 55 2 3 1 p 4 8 6 77 1 6 5 8 3 p 4 26 8 7 2 3 1 4 5 p

P 5 2 8 4 6 3 7 13 4 1 P 7 5 6 2 8

Solutions 215


3 8 7 n 4 1 6 2 52 n 5 6 8 7 4 3 16 1 4 5 2 3 8 7 n

n 3 8 4 7 2 1 5 64 2 6 8 1 5 3 n 75 7 1 3 6 n 2 4 81 6 n 2 5 4 7 8 37 4 3 1 n 8 5 6 28 5 2 7 3 6 n 1 4


8 5 7 2 1 n 4 3 63 n 2 6 4 7 8 5 11 6 4 3 5 8 n 7 2n 4 1 5 8 2 3 6 75 3 6 7 n 4 2 1 82 7 8 1 6 3 5 n 47 8 5 n 2 6 1 4 34 1 3 8 7 5 6 2 n6 2 n 4 3 1 7 8 5


7 p 8 3 2 1 6 5 43 6 1 7 4 5 8 P 25 2 4 6 p 8 7 1 31 4 P 5 8 3 2 7 62 3 7 4 6 P 1 8 56 8 5 1 7 2 4 3 P

p 5 6 2 1 7 3 4 88 1 2 p 3 4 5 6 74 7 3 8 5 6 P 2 1


7 1 4 2 8 k 6 5 32 8 5 4 6 3 1 q 76 q 3 1 7 5 8 4 21 7 2 5 3 6 4 8 k5 4 6 k 2 8 7 3 18 3 k 7 1 4 2 6 53 6 1 8 5 7 q 2 4

q 5 7 6 4 2 3 1 84 2 8 3 k 1 5 7 6


1 8 6 4 2 n 3 7 52 6 4 n 8 1 7 5 33 5 2 8 1 4 n 6 75 7 1 2 6 8 4 3 n6 n 3 1 7 5 2 4 88 4 7 5 3 2 1 n 6n 1 5 3 4 7 6 8 24 3 n 7 5 6 8 2 17 2 8 6 n 3 5 1 4


8 6 Q 5 4 1 7 2 33 2 5 8 6 7 4 1 N4 1 7 2 3 N 6 5 8N 7 6 1 2 5 3 8 45 8 4 3 7 6 1 N 22 3 1 4 N 8 5 6 76 5 3 N 8 4 2 7 11 4 8 7 5 2 N 3 67 N 2 6 1 3 8 4 5

216 Solutions


p 2 3 7 1 6 4 8 56 5 4 8 3 2 P 7 11 8 7 5 p 4 6 3 22 4 6 1 5 3 8 P 78 P 5 4 2 7 3 1 63 7 1 6 8 p 5 2 44 3 p 2 7 5 1 6 85 1 2 3 6 8 7 4 p7 6 8 P 4 1 2 5 3


4 2 8 n 1 6 3 7 56 n 7 5 3 8 2 1 41 3 5 7 2 4 n 8 63 8 1 2 6 7 5 4 n2 5 4 1 n 3 8 6 77 6 n 8 4 5 1 3 2n 4 2 6 8 1 7 5 38 7 6 3 5 2 4 n 15 1 3 4 7 n 6 2 8


7 8 1 4 3 2 5 p 62 6 5 1 P 8 7 4 3P 4 3 6 7 5 8 1 26 7 P 8 4 3 1 2 58 3 2 5 6 1 4 7 P1 5 4 7 2 P 3 6 84 2 8 p 5 7 6 3 15 P 7 3 1 6 2 8 43 1 6 2 8 4 P 5 7


2 1 8 3 6 7 5 N 4Q 3 6 4 5 1 8 7 24 5 7 8 N 2 3 1 68 7 1 2 3 N 6 4 56 4 2 5 7 8 N 3 15 N 3 1 4 6 2 8 73 8 5 6 1 4 7 2 N7 6 4 N 2 3 1 5 81 2 N 7 8 5 4 6 3


3 8 5 2 4 1 6 7 p2 1 P 6 7 5 4 3 86 4 7 3 p 8 1 2 5P 6 1 5 8 3 7 4 27 2 3 4 6 p 8 5 14 5 8 7 1 2 3 p 61 P 2 8 3 4 5 6 75 3 6 1 2 7 P 8 48 7 4 P 5 6 2 1 3


5 k 1 6 8 2 7 4 37 6 3 5 1 4 8 2 k8 4 2 q 3 7 5 1 6k 1 7 8 2 6 4 3 52 3 6 1 4 5 k 7 84 5 8 7 q 3 2 6 13 7 k 2 6 8 1 5 46 8 5 4 7 1 3 k 21 2 4 3 5 q 6 8 7

Solutions 217


3 7 2 Q 1 5 8 6 4N 1 6 8 4 2 3 5 74 5 8 7 6 3 N 1 21 4 N 3 5 8 7 2 66 3 7 1 2 4 5 8 N2 8 5 6 N 7 4 3 17 6 1 5 3 N 2 4 85 N 4 2 8 6 1 7 38 2 3 4 7 1 6 N 5


3 6 7 2 8 5 4 1 N1 N 2 3 4 7 8 5 64 5 8 1 N 6 7 2 32 4 5 7 3 N 6 8 18 3 1 6 5 4 N 7 26 7 N 8 2 1 5 3 45 2 6 N 7 3 1 4 8N 8 4 5 1 2 3 6 77 1 3 4 6 8 2 N 5


4 6 2 8 5 N 1 7 33 8 N 1 2 5 7 4 61 3 4 7 6 8 5 N 25 7 6 3 8 2 4 1 N2 1 7 5 N 3 8 6 48 N 1 2 4 6 3 5 7N 4 5 6 3 7 2 8 16 5 3 4 7 1 N 2 87 2 8 N 1 4 6 3 5


5 1 7 N 6 8 3 2 43 8 6 2 4 7 1 N 5N 2 4 5 3 1 6 7 87 5 2 1 N 3 8 4 66 4 1 8 7 5 2 3 N8 3 N 4 2 6 5 1 74 7 8 6 1 2 N 5 32 6 3 7 5 N 4 8 11 N 5 3 8 4 7 6 2


3 7 6 2 5 1 8 N 45 1 2 N 4 8 6 3 78 4 N 3 7 6 2 1 57 N 5 1 8 3 4 6 24 6 3 5 N 2 7 8 11 2 8 4 6 7 3 5 N

N 3 7 6 1 4 5 2 82 5 4 8 3 N 1 7 66 8 1 7 2 5 N 4 3


4 3 6 8 p 7 1 5 22 7 p 5 6 1 4 3 85 1 8 3 4 2 p 7 68 6 4 p 7 3 2 1 53 p 5 2 1 4 8 6 71 2 7 6 8 5 3 p 46 4 3 7 2 p 5 8 1P 8 1 4 5 6 7 2 37 5 2 1 3 8 6 4 P

218 Solutions


8 5 2 1 6 3 7 n 45 4 7 6 2 n 3 1 87 n 1 2 3 5 4 8 61 6 3 n 4 7 8 5 24 2 6 3 n 8 1 7 56 3 n 8 1 2 5 4 7n 1 8 7 5 4 6 2 32 7 4 5 8 6 n 3 13 8 5 4 7 1 2 6 n


3 7 5 6 2 4 N 1 81 4 N 8 7 3 6 5 26 8 2 N 1 5 7 4 32 6 4 5 N 7 8 3 1N 5 8 3 4 1 2 6 77 3 1 2 8 6 4 N 58 1 6 4 5 2 3 7 N5 Q 3 7 6 8 1 2 44 2 7 1 3 N 5 8 6


6 n 1 8 5 7 2 3 45 3 8 n 2 4 7 1 67 2 4 3 6 1 8 5 n8 4 3 5 1 6 n 7 22 7 6 4 n 3 1 8 5n 1 5 7 8 2 6 4 31 5 n 2 4 8 3 6 74 8 7 6 3 n 5 2 13 6 2 1 7 5 4 n 8


6 4 2 p 1 3 5 7 88 p 7 4 5 6 3 2 13 5 1 7 2 8 4 p 65 1 4 2 6 P 7 8 3p 6 8 5 3 7 2 1 42 7 3 1 8 4 p 6 54 2 6 8 7 5 1 3 P1 3 P 6 4 2 8 5 77 8 5 3 P 1 6 4 2


2 4 5 1 6 q 3 8 76 1 k 3 7 8 5 4 27 8 3 5 2 4 1 k 6

q 6 4 7 1 5 2 3 85 2 1 4 8 3 7 6 k8 3 7 2 k 6 4 1 54 5 6 8 3 2 q 7 11 q 2 6 4 7 8 5 33 7 8 k 5 1 6 2 4


4 1 6 3 Q 5 8 2 78 Q 7 6 1 2 4 3 55 2 3 8 4 7 1 Q 61 6 Q 7 2 8 3 5 42 7 8 4 5 3 Q 6 13 5 4 Q 6 1 2 7 8Q 8 2 5 7 4 6 1 37 4 1 2 3 6 5 8 Q

6 3 5 1 8 Q 7 4 2

Solutions 219


5 7 3 N 8 1 6 2 4N 4 6 7 2 3 8 1 51 8 2 4 6 5 7 N 36 1 8 5 7 2 3 4 N7 2 4 3 N 6 1 5 83 N 5 1 4 8 2 6 74 5 1 6 3 7 N 8 22 6 7 8 5 N 4 3 18 3 N 2 1 4 5 7 6


6 2 4 k 1 8 7 3 5

q 3 8 4 5 7 1 2 67 5 1 2 6 3 k 4 85 k 7 8 3 1 2 6 43 1 2 6 4 5 8 q 74 8 6 7 2 k 3 5 12 4 3 1 7 6 5 8 k1 6 q 5 8 2 4 7 38 7 5 3 k 4 6 1 2


8 5 2 4 6 3 n 7 16 7 1 2 3 5 4 8 n

n 4 7 6 2 1 8 5 31 3 5 8 7 4 2 n 63 n 6 5 4 8 1 2 72 1 4 n 8 7 6 3 57 2 3 1 n 6 5 4 85 8 n 3 1 2 7 6 44 6 8 7 5 n 3 1 2


5 8 3 7 4 k 1 2 66 7 1 8 2 3 5 4 k2 4 k 1 6 5 3 7 84 5 8 6 3 1 7 q 23 q 2 4 8 7 6 5 11 6 7 k 5 2 8 3 4k 3 5 2 1 8 4 6 78 2 6 3 7 4 q 1 57 1 4 5 k 6 2 8 3


7 8 5 1 2 3 4 6 N6 1 4 N 8 5 7 2 33 2 N 7 4 6 1 8 52 5 6 3 1 N 8 7 48 7 1 6 5 4 N 3 24 Q 3 8 7 2 5 1 61 3 2 4 N 7 6 5 85 4 8 2 6 1 3 N 7N 6 7 5 3 8 2 4 1


6 8 4 Q 2 3 5 1 7Q 3 2 5 7 1 4 6 85 1 7 6 8 4 2 3 Q

3 6 5 8 1 Q 7 4 24 2 Q 7 5 6 3 8 18 7 1 3 4 2 Q 5 67 Q 8 4 6 5 1 2 32 4 6 1 3 7 8 Q 51 5 3 2 Q 8 6 7 4

220 Solutions


2 5 7 4 1 6 p 3 88 4 3 7 P 5 6 1 21 6 p 3 2 8 4 5 75 7 8 1 4 P 2 6 36 3 1 5 7 2 8 p 44 p 2 8 6 3 5 7 17 2 5 P 8 1 3 4 63 8 4 6 5 7 1 2 P

P 1 6 2 3 4 7 8 5


N 5 7 2 4 8 6 3 13 8 2 1 5 6 4 N 71 6 4 N 3 7 8 5 27 3 6 5 N 2 1 8 48 1 5 3 7 4 2 6 N4 2 N 6 8 1 5 7 35 7 1 8 2 N 3 4 66 4 3 7 1 5 N 2 82 N 8 4 6 3 7 1 5


6 2 8 4 3 5 N 1 73 N 1 8 7 6 5 4 27 4 5 2 N 1 3 6 84 5 2 7 8 N 6 3 11 7 6 5 2 3 4 8 N

N 8 3 6 1 4 2 7 52 3 7 N 6 8 1 5 45 6 N 1 4 7 8 2 38 1 4 3 5 2 7 N 6


7 6 N 5 8 1 3 4 23 2 1 N 7 4 5 6 88 5 4 2 3 6 1 7 Q

N 8 6 3 4 5 7 2 12 3 5 7 1 N 6 8 41 4 7 6 2 8 N 3 54 N 3 8 5 7 2 1 66 7 8 1 N 2 4 5 35 1 2 4 6 3 8 N 7


N 6 5 3 4 2 7 1 81 8 4 6 N 7 5 2 32 7 3 5 8 1 6 4 N3 N 7 4 1 5 2 8 65 1 6 8 2 3 N 7 44 2 8 7 6 N 1 3 57 3 N 1 5 4 8 6 26 4 2 N 7 8 3 5 18 5 1 2 3 6 4 N 7


5 1 3 2 n 8 7 6 48 2 n 7 4 6 3 5 16 4 7 3 5 1 n 8 22 8 5 6 1 3 4 7 n

n 7 1 5 8 4 2 3 64 3 6 n 7 2 8 1 51 n 8 4 6 7 5 2 33 6 4 8 2 5 1 n 77 5 2 1 3 n 6 4 8

Solutions 221


4 1 2 7 3 N 8 5 68 7 N 6 1 5 4 3 25 6 3 4 2 8 1 7 N

N 4 1 8 7 3 6 2 52 8 5 N 6 1 7 4 36 3 7 5 4 2 N 8 11 5 6 2 8 4 3 N 77 N 4 3 5 6 2 1 83 2 8 1 N 7 5 6 4


N 8 4 3 7 5 1 2 61 5 6 2 N 4 3 7 87 3 2 8 6 1 5 N 44 2 1 6 8 7 N 3 53 7 8 1 5 N 4 6 26 N 5 4 2 3 7 8 18 1 7 5 3 2 6 4 Q5 6 3 N 4 8 2 1 72 4 N 7 1 6 8 5 3


Q 1 2 3 4 6 7 8 55 8 3 1 Q 7 4 2 64 6 7 8 5 2 1 3 Q3 Q 8 2 7 4 6 5 11 2 6 5 3 Q 8 4 77 5 4 6 8 1 3 Q 26 4 Q 7 2 3 5 1 82 7 5 4 1 8 Q 6 38 3 1 Q 6 5 2 7 4


5 3 Q 4 7 8 6 1 28 4 1 6 3 2 5 7 Q2 7 6 1 5 Q 3 4 83 Q 5 2 4 1 8 6 76 2 4 8 Q 7 1 3 51 8 7 5 6 3 Q 2 4Q 1 8 3 2 4 7 5 67 6 2 Q 1 5 4 8 34 5 3 7 8 6 2 Q 1


3 k 7 4 8 6 1 5 26 1 4 5 7 2 k 8 38 5 2 q 3 1 4 6 77 6 1 8 2 5 3 4 q

k 3 8 1 6 4 7 2 52 4 5 3 k 7 8 1 64 2 q 6 1 3 5 7 85 7 3 2 4 8 6 k 11 8 6 7 5 q 2 3 4


4 8 3 1 6 5 N 2 71 7 2 3 8 N 5 4 6N 6 5 4 2 7 3 8 16 4 7 5 1 8 2 3 N5 3 N 2 7 4 1 6 82 1 8 N 3 6 4 7 58 5 4 6 N 2 7 1 33 2 6 7 5 1 8 N 47 N 1 8 4 3 6 5 2

222 Solutions


7 N 4 3 5 1 6 8 21 5 6 2 8 7 N 3 43 8 2 N 6 4 5 7 15 7 8 4 N 2 1 6 34 6 3 7 1 5 2 N 8N 2 1 8 3 6 7 4 58 1 5 6 4 N 3 2 76 4 7 1 2 3 8 5 N2 3 N 5 7 8 4 1 6


5 6 8 7 n 2 1 4 37 2 3 4 6 1 n 8 5n 1 4 8 3 5 2 6 71 7 n 2 5 8 6 3 44 8 6 1 7 3 5 2 n2 3 5 6 4 n 7 1 86 5 1 3 8 7 4 n 28 4 7 n 2 6 3 5 13 n 2 5 1 4 8 7 6


8 1 Q 2 4 6 5 7 32 5 4 7 3 Q 8 6 17 3 6 8 5 1 4 Q 25 2 1 4 Q 7 6 3 83 Q 7 6 1 8 2 4 54 6 8 5 2 3 7 1 Q1 7 2 3 8 4 Q 5 66 8 3 Q 7 5 1 2 4

Q 4 5 1 6 2 3 8 7


5 Q 7 4 3 6 8 1 28 4 6 2 7 1 Q 5 31 2 3 8 Q 5 4 6 77 8 4 6 2 3 1 Q 5

Q 6 2 5 1 8 7 3 43 1 5 Q 4 7 6 2 84 5 8 3 6 Q 2 7 12 7 Q 1 5 4 3 8 66 3 1 7 8 2 5 4 Q


4 6 1 7 5 3 8 2 N3 8 7 1 2 N 4 6 52 5 N 4 6 8 1 7 38 N 4 6 1 2 3 5 76 3 5 8 4 7 N 1 21 7 2 N 3 5 6 4 85 2 6 3 N 4 7 8 1N 4 8 2 7 1 5 3 67 1 3 5 8 6 2 N 4


3 6 5 4 N 7 2 1 84 1 8 6 2 3 5 7 N2 7 N 5 8 1 4 6 35 N 6 3 1 2 8 4 78 2 3 7 4 N 1 5 61 4 7 8 5 6 N 3 27 5 2 1 6 8 3 N 46 8 4 N 3 5 7 2 1N 3 1 2 7 4 6 8 5

Solutions 223


4 7 2 5 1 3 n 8 65 1 8 3 n 6 4 7 26 3 1 n 8 4 5 2 73 8 5 2 6 n 7 4 1n 6 7 4 2 5 8 1 32 4 6 1 5 7 3 n 87 n 4 8 3 2 1 6 58 2 3 7 4 1 6 5 n1 5 n 6 7 8 2 3 4


6 5 8 4 k 2 7 1 3

q 3 7 8 5 1 4 6 24 1 2 3 7 6 q 8 55 4 k 1 2 7 6 3 82 7 3 6 8 k 1 5 48 6 1 5 3 4 2 7 k7 8 4 k 1 3 5 2 63 2 6 7 4 5 8 q 11 q 5 2 6 8 3 4 7


8 4 3 6 2 1 5 7 Q5 1 2 Q 7 8 6 3 47 Q 6 5 4 3 2 1 81 7 8 4 3 6 Q 5 26 3 Q 1 5 2 8 4 72 5 4 7 8 Q 3 6 13 2 1 8 6 4 7 Q 5

Q 8 5 3 1 7 4 2 64 6 7 2 Q 5 1 8 3


5 3 7 8 4 2 n 6 1n 8 2 6 3 1 4 7 51 4 6 5 7 n 3 2 88 n 5 7 2 3 1 4 63 6 4 1 5 8 7 n 27 2 1 n 6 4 8 5 32 7 3 4 1 5 6 8 n4 5 8 3 n 6 2 1 76 1 n 2 8 7 5 3 4


5 6 2 8 7 n 4 1 3n 8 4 3 6 1 7 5 23 7 1 2 5 4 n 6 84 n 7 1 3 5 8 2 61 2 5 6 n 8 3 4 76 3 8 4 2 7 1 n 58 5 6 n 4 3 2 7 17 4 3 5 1 2 6 8 n2 1 n 7 8 6 5 3 4


4 3 2 p 5 1 8 7 65 P 1 6 7 8 3 2 46 7 8 4 2 3 P 5 13 8 5 1 4 2 7 6 p2 6 p 8 3 7 4 1 57 1 4 5 6 p 2 3 88 2 6 7 1 4 5 P 3P 5 3 2 8 6 1 4 71 4 7 3 P 5 6 8 2

224 Solutions


2 4 6 5 3 7 n 8 13 n 5 8 6 1 4 2 78 1 7 2 4 n 3 5 6n 6 8 3 1 2 7 4 55 7 2 4 n 6 1 3 81 3 4 7 8 5 6 n 27 2 1 n 5 4 8 6 34 5 3 6 7 8 2 1 n6 8 n 1 2 3 5 7 4


4 3 2 8 1 k 5 7 66 7 1 5 2 3 8 q 45 8 q 7 4 6 1 2 37 1 8 6 k 4 3 5 2k 6 3 1 5 2 4 8 72 4 5 3 7 8 6 1 q

3 5 7 k 6 1 2 4 81 2 6 4 8 7 k 3 58 q 4 2 3 5 7 6 1


3 n 2 4 5 7 6 8 15 1 8 n 2 6 7 3 44 6 7 8 1 3 5 2 n8 5 1 2 3 n 4 6 76 2 4 1 7 8 3 n 5n 7 3 5 6 4 2 1 82 8 n 6 4 5 1 7 31 3 5 7 8 2 n 4 67 4 6 3 n 1 8 5 2


8 p 7 6 4 1 5 3 21 5 3 8 p 2 4 7 62 4 6 7 5 3 1 8 p

P 6 1 4 3 8 2 5 74 3 5 1 2 7 6 p 87 2 8 5 6 p 3 4 15 8 4 P 1 6 7 2 33 1 p 2 7 4 8 6 56 7 2 3 8 5 P 1 4


5 1 3 4 8 7 p 2 64 6 2 p 3 5 8 7 1P 8 7 2 1 6 5 4 33 2 P 6 4 1 7 5 81 7 4 8 5 p 6 3 28 5 6 3 7 2 1 P 47 4 1 5 2 8 3 6 p6 3 8 7 p 4 2 1 52 P 5 1 6 3 4 8 7


8 N 3 7 2 4 5 1 64 1 7 3 5 6 8 2 N6 5 2 1 8 N 4 7 37 3 6 8 1 5 N 4 21 2 N 4 3 7 6 5 85 4 8 N 6 2 7 3 12 8 4 5 N 1 3 6 73 7 1 6 4 8 2 Q 5N 6 5 2 7 3 1 8 4

Solutions 225


6 p 2 7 3 8 1 4 51 4 7 6 5 p 8 2 35 3 8 2 1 4 7 6 P3 7 p 8 6 2 5 1 48 1 4 5 p 7 2 3 62 6 5 3 4 1 p 8 7P 8 6 4 2 5 3 7 14 2 1 P 7 3 6 5 87 5 3 1 8 6 4 P 2


7 4 3 8 1 6 2 5 Q8 6 5 3 2 Q 1 4 72 1 Q 4 7 5 6 8 3Q 7 4 2 6 8 3 1 56 8 1 7 5 3 4 Q 25 3 2 1 Q 4 7 6 84 Q 7 5 3 1 8 2 61 2 6 Q 8 7 5 3 43 5 8 6 4 2 Q 7 1


1 2 5 4 7 8 p 6 34 7 3 6 P 1 2 5 86 p 8 5 2 3 4 7 15 4 1 7 6 P 8 3 28 6 7 2 3 4 1 P 5p 3 2 8 1 5 7 4 67 1 p 3 8 6 5 2 42 5 6 1 4 7 3 8 p3 8 4 P 5 2 6 1 7


8 N 7 5 1 2 4 3 64 2 5 7 6 3 N 1 81 6 3 N 8 4 7 2 53 8 1 2 N 7 6 5 42 7 6 4 5 8 3 N 15 4 N 6 3 1 2 8 77 5 8 3 4 N 1 6 2N 1 4 8 2 6 5 7 36 3 2 1 7 5 8 4 N


Q 5 8 3 1 4 6 7 27 3 4 2 8 6 Q 1 52 1 6 Q 5 7 3 8 46 4 2 8 3 Q 1 5 75 8 7 6 4 1 2 3 Q3 Q 1 7 2 5 8 4 64 2 5 1 Q 3 7 6 81 6 Q 4 7 8 5 2 38 7 3 5 6 2 4 Q 1


8 4 6 7 5 1 3 q 25 1 k 8 3 2 7 6 47 3 2 k 6 4 8 5 1

q 8 3 6 1 5 4 2 76 2 7 4 q 8 1 3 54 5 1 3 2 7 6 8 q

3 k 4 2 7 6 5 1 82 7 5 1 8 3 k 4 61 6 8 5 4 k 2 7 3

226 Solutions


6 5 2 1 4 Q 8 7 37 Q 4 3 2 8 5 6 11 3 8 7 6 5 2 4 Q3 6 7 2 Q 4 1 5 88 2 Q 6 5 1 7 3 44 1 5 8 7 3 6 Q 25 8 1 Q 3 7 4 2 62 7 3 4 8 6 Q 1 5

Q 4 6 5 1 2 3 8 7


1 3 2 N 8 4 7 6 58 6 4 5 2 3 N 7 14 N 7 1 6 2 3 5 86 8 5 4 3 7 2 1 N7 5 3 2 1 N 6 8 42 7 N 3 5 1 8 4 63 1 8 6 7 5 4 N 2N 2 1 8 4 6 5 3 75 4 6 7 N 8 1 2 3


1 4 3 7 2 5 n 8 67 n 6 1 8 4 3 2 52 8 5 3 6 n 7 4 1n 5 2 4 3 7 1 6 88 3 4 6 1 2 5 7 n6 1 7 n 5 8 4 3 25 7 1 8 4 6 2 n 34 2 8 5 n 3 6 1 73 6 n 2 7 1 8 5 4


1 4 5 7 8 p 3 6 22 6 3 1 5 4 7 8 P

P 8 7 6 2 3 4 1 53 2 P 4 7 8 1 5 64 5 1 3 P 6 8 2 78 7 6 5 1 2 p 4 37 P 2 8 6 1 5 3 46 1 4 P 3 5 2 7 85 3 8 2 4 7 6 P 1


4 5 3 2 k 1 8 7 67 2 8 6 5 4 1 3 k6 q 1 7 3 8 4 5 21 4 5 8 6 2 7 q 3k 6 2 4 7 3 5 8 13 8 7 5 1 k 6 2 45 7 k 1 2 6 3 4 82 1 4 3 8 5 k 6 78 3 6 q 4 7 2 1 5


1 4 7 2 5 6 n 3 88 1 6 3 n 7 5 4 25 3 n 8 1 2 4 6 77 2 3 6 8 5 1 n 46 n 4 7 2 8 3 1 54 6 8 5 3 1 2 7 n

n 5 2 4 7 3 6 8 12 8 1 n 6 4 7 5 33 7 5 1 4 n 8 2 6

Solutions 227


2 3 7 4 N 1 6 8 56 5 1 2 8 3 7 N 48 N 4 5 7 6 2 3 17 1 N 6 5 8 3 4 23 6 8 7 2 4 1 5 N4 2 5 3 1 N 8 7 65 8 2 1 4 7 N 6 31 7 6 N 3 5 4 2 8N 4 3 8 6 2 5 1 7


4 1 3 p 2 5 8 7 66 8 7 4 1 3 2 P 5P 5 2 8 7 6 4 3 18 2 4 6 P 7 1 5 31 3 P 5 4 2 7 6 85 7 6 1 3 8 P 4 22 6 8 7 5 4 3 1 P7 p 5 3 8 1 6 2 43 4 1 2 6 P 5 8 7


4 N 8 2 3 5 6 7 15 7 3 1 8 6 4 N 21 6 2 7 N 4 3 5 82 3 6 N 1 8 5 4 7N 5 4 6 7 2 1 8 37 8 1 4 5 3 2 6 N3 1 N 5 6 7 8 2 48 2 5 3 4 N 7 1 66 4 7 8 2 1 N 3 5


1 7 5 4 N 8 6 3 23 8 6 N 2 7 1 4 54 6 2 5 8 3 N 1 78 3 7 2 4 6 5 N 17 N 1 8 5 2 3 6 42 1 N 3 7 5 4 8 66 5 4 7 1 N 8 2 35 4 8 6 3 1 2 7 N

N 2 3 1 6 4 7 5 8


p 8 7 5 3 6 1 4 23 1 4 8 p 2 5 6 72 5 6 7 4 1 3 8 P4 P 8 3 1 5 7 2 67 3 5 2 6 4 p 1 81 6 2 p 8 7 4 3 58 2 1 4 5 P 6 7 36 7 P 1 2 3 8 5 45 4 3 6 7 8 2 P 1


5 6 7 4 1 8 p 3 22 3 P 6 5 7 4 1 88 1 4 3 p 2 5 7 67 P 2 1 3 5 8 6 43 4 8 7 2 6 1 p 56 5 1 p 8 4 7 2 34 2 3 5 7 1 6 8 p

P 7 6 8 4 3 2 5 11 8 5 2 6 P 3 4 7

228 Solutions


6 8 3 1 4 2 5 7 N1 7 4 N 3 5 6 2 8N 5 2 7 6 8 3 1 45 4 6 8 7 1 2 N 32 3 7 5 N 6 4 8 18 N 1 3 2 4 7 6 53 1 8 2 5 7 N 4 67 6 5 4 1 N 8 3 24 2 N 6 8 3 1 5 7


6 Q 5 4 8 3 1 7 27 8 2 1 5 6 Q 3 43 1 4 2 Q 7 6 5 88 2 1 3 6 5 4 Q 7Q 5 3 8 7 4 2 1 64 7 6 Q 2 1 3 8 52 6 8 7 3 Q 5 4 15 4 Q 6 1 8 7 2 31 3 7 5 4 2 8 6 Q


4 5 7 1 Q 3 2 6 86 Q 2 8 4 5 1 7 38 3 1 7 2 6 4 5 Q

1 4 6 2 7 Q 3 8 53 8 Q 4 5 1 6 2 77 2 5 6 3 8 Q 4 15 6 3 Q 8 2 7 1 4Q 1 4 5 6 7 8 3 22 7 8 3 1 4 5 Q 6


5 6 4 1 2 7 8 3 n3 7 2 4 8 5 n 1 6n 8 1 7 6 3 5 4 26 3 8 n 5 4 1 2 74 n 6 3 1 2 7 8 51 2 5 8 7 n 3 6 47 5 3 6 4 8 2 n 12 4 n 5 3 1 6 7 88 1 7 2 n 6 4 5 3


2 N 8 7 4 1 5 6 34 1 7 3 6 5 2 8 N5 6 3 8 2 N 7 4 1N 8 5 1 7 6 4 3 26 7 4 5 3 2 1 N 81 3 2 4 N 8 6 5 78 4 1 N 5 7 3 2 63 2 N 6 1 4 8 7 57 5 6 2 8 3 Q 1 4


3 4 6 5 n 7 1 8 22 1 n 4 8 3 7 6 55 7 8 1 2 6 4 3 n8 5 1 2 6 4 n 7 34 n 2 3 7 1 8 5 66 3 7 n 5 8 2 1 4n 8 5 6 1 2 3 4 71 2 4 7 3 5 6 n 87 6 3 8 4 n 5 2 1

Solutions 229


3 4 1 6 k 7 2 5 87 2 k 8 5 4 1 6 36 8 5 1 2 3 q 4 7

q 3 7 4 8 5 6 1 21 6 2 3 7 k 4 8 58 5 4 2 1 6 7 3 q2 q 3 5 6 1 8 7 45 1 8 7 4 2 3 k 64 7 6 k 3 8 5 2 1


8 4 6 1 q 5 3 7 2

q 7 3 8 2 6 1 5 42 5 1 4 7 3 k 8 67 6 k 3 4 1 5 2 83 8 2 5 6 k 7 4 15 1 4 7 8 2 6 3 k1 2 8 q 5 7 4 6 36 3 5 2 1 4 8 q 74 k 7 6 3 8 2 1 5


2 6 7 3 n 4 8 1 51 8 4 5 7 2 n 3 6n 5 3 1 6 8 2 7 43 4 6 n 8 5 1 2 77 n 1 2 4 3 6 5 88 2 5 7 1 6 3 4 n4 7 n 8 3 1 5 6 25 1 8 6 2 7 4 n 36 3 2 4 5 n 7 8 1


6 1 7 5 8 3 n 4 25 n 3 7 2 4 8 1 64 8 2 1 6 n 3 5 7n 2 1 4 7 6 5 3 83 6 4 8 n 5 2 7 18 7 5 3 1 2 6 n 42 5 8 n 4 7 1 6 37 3 6 2 5 1 4 8 n1 4 n 6 3 8 7 2 5


p 4 3 2 1 8 7 6 58 1 5 4 7 6 P 3 26 7 2 5 P 3 8 4 13 P 8 1 6 5 4 2 75 6 4 P 2 7 3 1 87 2 1 3 8 4 6 5 p2 8 p 6 4 1 5 7 31 3 6 7 5 p 2 8 44 5 7 8 3 2 1 P 6


2 7 3 1 5 6 N 4 84 6 5 N 3 8 2 7 11 8 N 4 7 2 6 5 37 5 4 3 2 1 8 Q 6N 3 1 6 8 7 4 2 56 2 8 5 N 4 1 3 73 4 7 8 1 N 5 6 28 N 2 7 6 5 3 1 45 1 6 2 4 3 7 8 N

230 Solutions


6 3 2 5 8 1 n 7 4n 8 4 3 6 7 5 1 27 1 5 4 2 n 6 3 88 n 1 7 5 4 2 6 35 7 3 2 n 6 4 8 14 2 6 1 3 8 7 n 53 4 n 8 7 5 1 2 62 5 7 6 1 3 8 4 n1 6 8 n 4 2 3 5 7


6 8 3 7 5 1 2 N 47 1 N 2 6 8 5 4 35 4 6 N 3 2 8 1 7N 3 4 1 7 5 6 8 22 6 8 5 1 7 4 3 N8 7 2 3 4 N 1 6 54 5 1 8 2 3 N 7 63 N 5 4 8 6 7 2 11 2 7 6 N 4 3 5 8


7 6 8 1 N 5 4 2 34 2 1 6 3 8 7 N 5N 5 3 2 7 4 6 1 83 N 6 7 5 1 2 8 45 4 2 8 6 N 3 7 11 8 7 3 4 2 5 6 N2 3 5 N 1 6 8 4 76 7 N 4 8 3 1 5 28 1 4 5 2 7 N 3 6


N 6 1 2 3 7 8 4 57 3 2 8 5 4 1 N 68 4 5 N 7 6 3 2 15 2 8 4 N 3 6 1 74 7 6 3 8 1 2 5 N3 1 N 5 6 2 7 8 42 8 4 7 1 N 5 6 31 5 3 6 4 8 N 7 26 N 7 1 2 5 4 3 8


7 2 5 8 n 3 1 6 44 3 n 2 1 6 8 5 71 6 8 7 5 4 n 3 23 8 6 4 2 1 5 7 n

n 4 2 3 7 5 6 8 15 1 7 n 6 8 2 4 36 n 4 5 3 2 7 1 82 5 3 1 8 7 4 n 68 7 1 6 4 n 3 2 5


6 7 8 1 2 3 4 5 Q4 2 5 6 Q 7 1 8 3Q 1 3 8 5 4 6 2 71 3 7 5 6 2 8 Q 48 4 6 Q 7 1 2 3 55 Q 2 4 3 8 7 1 67 8 1 3 4 5 Q 6 22 5 Q 7 1 6 3 4 83 6 4 2 8 Q 5 7 1

Solutions 231


6 1 7 2 5 4 8 3 n1 n 6 4 3 5 7 2 87 8 5 3 1 2 4 n 6n 4 1 8 2 3 6 7 53 2 n 6 7 1 5 8 42 5 8 n 4 7 3 6 14 6 3 7 8 n 1 5 28 7 4 5 n 6 2 1 35 3 2 1 6 8 n 4 7


4 3 5 7 6 1 2 8 N6 1 8 4 2 Q 7 5 32 N 7 5 3 8 6 4 18 6 N 2 7 5 1 3 45 4 2 6 1 3 8 N 73 7 1 8 N 4 5 6 27 2 4 N 8 6 3 1 51 5 6 3 4 2 N 7 8N 8 3 1 5 7 4 2 6


4 5 N 7 8 6 2 3 11 7 2 N 5 3 8 4 63 6 8 4 2 1 N 7 52 4 7 1 3 5 6 N 85 Q 6 2 4 8 7 1 38 1 3 6 7 N 5 2 46 2 1 5 N 4 3 8 7N 8 4 3 6 7 1 5 27 3 5 8 1 2 4 6 N


8 Q 4 1 5 7 6 2 36 1 3 4 Q 2 5 8 72 7 5 8 6 3 1 Q 4

Q 5 2 3 8 6 7 4 17 3 1 2 4 5 8 6 Q4 6 8 7 1 Q 3 5 23 4 Q 6 7 8 2 1 51 2 6 5 3 4 Q 7 85 8 7 Q 2 1 4 3 6


5 8 6 1 3 4 n 2 77 3 4 6 n 2 1 5 8n 2 1 8 7 5 4 6 34 7 2 3 5 n 6 8 11 n 5 2 6 8 7 3 48 6 3 7 4 1 2 n 52 5 8 n 1 7 3 4 63 4 7 5 2 6 8 1 n6 1 n 4 8 3 5 7 2


7 4 3 2 n 6 1 8 51 6 5 8 4 2 n 3 7n 3 2 7 8 5 6 4 15 8 4 3 1 n 7 6 24 n 8 5 3 7 2 1 63 1 6 4 2 8 5 7 n8 2 7 n 6 1 3 5 42 7 1 6 5 4 8 n 36 5 n 1 7 3 4 2 8

232 Solutions


7 4 Q 8 2 6 3 5 13 1 2 5 4 Q 8 7 68 5 6 1 3 7 2 Q 45 6 4 2 Q 8 1 3 7Q 2 7 3 5 1 4 6 81 3 8 6 7 4 5 2 Q6 8 3 7 1 5 Q 4 22 Q 1 4 6 3 7 8 54 7 5 Q 8 2 6 1 3


6 4 2 1 5 7 8 N 35 3 7 8 Q 4 6 2 1N 1 8 2 6 3 5 4 71 N 6 4 8 5 7 3 28 2 4 7 3 1 N 6 53 7 5 N 2 6 4 1 87 5 N 6 1 2 3 8 42 6 3 5 4 8 1 7 N4 8 1 3 7 N 2 5 6


2 8 7 1 4 3 6 n 53 4 5 7 2 n 1 6 84 1 n 8 6 5 7 3 2n 6 2 3 1 8 5 7 41 5 3 6 7 4 2 8 n6 3 8 2 5 7 n 4 15 2 4 n 8 6 3 1 77 n 1 4 3 2 8 5 68 7 6 5 n 1 4 2 3


8 2 4 7 3 N 5 6 11 6 3 2 8 5 N 4 75 N 7 6 4 1 2 3 8N 3 1 4 7 2 6 8 56 4 5 8 N 3 1 7 27 8 2 5 1 6 4 N 33 7 6 1 2 4 8 5 N2 5 8 N 6 7 3 1 44 1 N 3 5 8 7 2 6


7 2 1 4 3 8 5 N 63 N 8 7 6 5 1 4 26 4 5 1 N 2 3 8 72 5 7 N 8 6 4 1 38 1 4 2 7 3 N 6 5N 6 3 5 4 1 2 7 85 8 2 6 1 4 7 3 N4 3 N 8 2 7 6 5 11 7 6 3 5 N 8 2 4


1 2 N 7 4 6 5 3 84 3 5 8 1 N 2 6 78 7 6 5 3 2 4 1 N5 6 7 N 8 1 3 4 2N 4 2 6 7 3 8 5 13 1 8 2 5 4 7 N 67 8 3 1 N 5 6 2 42 Q 4 3 6 7 1 8 56 5 1 4 2 8 N 7 3

Solutions 233


5 2 7 3 n 1 6 8 44 3 1 8 6 2 n 7 5n 6 8 7 4 5 2 1 31 8 3 5 7 n 4 6 26 n 2 1 3 4 7 5 87 4 5 6 2 8 3 n 12 1 4 n 5 6 8 3 78 7 6 4 1 3 5 2 n3 5 n 2 8 7 1 4 6


5 1 8 6 2 4 Q 7 3Q 2 3 7 8 1 4 6 57 6 4 Q 5 3 1 8 28 5 1 3 4 7 2 Q 66 4 7 8 Q 2 3 5 12 3 Q 5 1 6 7 4 81 7 2 4 6 5 8 3 Q3 8 5 2 7 Q 6 1 44 Q 6 1 3 8 5 2 7


p 6 7 2 5 3 4 8 14 5 3 8 1 6 p 7 22 1 8 p 4 7 3 5 66 P 1 4 3 8 7 2 53 8 5 6 7 2 1 4 P7 4 2 1 P 5 6 3 81 3 p 5 2 4 8 6 75 7 6 3 8 1 2 p 48 2 4 7 6 P 5 1 3


7 5 1 4 2 N 6 8 38 3 N 5 6 7 2 1 44 6 2 3 8 1 7 5 N1 4 7 6 5 3 8 N 25 2 3 7 N 8 1 4 66 N 8 2 1 4 5 3 72 7 4 8 3 5 N 6 13 1 5 N 7 6 4 2 8N 8 6 1 4 2 3 7 5


6 N 7 4 1 8 3 2 51 3 2 7 N 5 6 4 88 5 4 2 6 3 1 7 N3 6 N 5 4 1 2 8 75 7 8 3 2 N 4 1 64 2 1 8 7 6 N 5 32 8 5 6 3 4 7 N 17 1 6 N 5 2 8 3 4N 4 3 1 8 7 5 6 2


3 1 4 2 7 N 5 6 8N 8 6 5 1 3 2 4 77 5 2 6 8 4 3 1 N8 2 N 1 3 7 6 5 41 4 3 N 6 5 8 7 26 7 5 4 2 8 N 3 15 6 7 8 4 2 1 N 34 N 8 3 5 1 7 2 62 3 1 7 Q 6 4 8 5

234 Solutions


7 1 5 2 3 6 4 8 n4 2 8 6 1 5 n 7 31 n 4 3 8 2 7 6 53 5 6 7 n 8 1 2 48 6 n 5 4 7 2 3 1n 4 7 8 2 1 3 5 66 3 2 1 5 4 8 n 75 8 3 4 7 n 6 1 22 7 1 n 6 3 5 4 8


4 2 6 N 8 1 5 3 77 3 1 4 5 2 8 N 6N 5 8 3 6 7 2 4 11 8 4 7 N 5 3 6 25 6 3 2 1 8 4 7 N2 N 7 6 4 3 1 8 58 4 5 1 7 6 N 2 36 1 2 8 3 N 7 5 43 7 N 5 2 4 6 1 8


2 N 3 7 1 8 6 5 46 5 1 3 4 2 N 7 84 8 7 5 6 N 3 1 21 3 4 2 N 6 5 8 7N 6 8 1 5 7 2 4 35 7 2 4 8 3 1 6 N3 1 5 N 7 4 8 2 68 4 N 6 2 1 7 3 57 2 6 8 3 5 4 Q 1


5 8 7 2 1 p 4 3 66 3 P 7 5 4 1 2 84 1 2 6 3 8 5 7 P2 p 3 1 7 5 8 6 47 6 5 4 8 2 3 P 18 4 1 3 p 6 2 5 71 2 8 5 6 7 p 4 3P 7 4 8 2 3 6 1 53 5 6 P 4 1 7 8 2


3 7 p 1 4 8 6 5 26 5 4 3 2 7 8 P 12 1 8 P 6 5 4 7 38 P 7 6 3 4 1 2 54 3 5 7 1 2 P 6 81 6 2 5 8 p 7 3 45 4 6 2 7 1 3 8 p

P 8 3 4 5 6 2 1 77 2 1 8 P 3 5 4 6


1 7 5 k 4 8 2 6 33 6 k 5 1 2 8 7 48 2 4 3 7 6 k 5 15 3 1 7 q 4 6 8 27 k 6 8 2 3 1 4 54 8 2 1 6 5 7 3 q

q 4 8 2 5 7 3 1 62 5 3 6 8 1 4 k 76 1 7 4 3 k 5 2 8

Solutions 235


3 1 8 5 4 Q 6 2 76 Q 4 1 2 7 8 5 32 7 5 3 8 6 1 4 Q4 8 7 2 Q 3 5 1 61 2 Q 4 6 5 3 7 85 3 6 8 7 1 4 Q 28 6 2 Q 5 4 7 3 17 4 3 6 1 2 Q 8 5Q 5 1 7 3 8 2 6 4


1 6 8 7 5 3 k 4 2

q 2 3 6 4 1 8 5 77 4 5 2 8 q 1 6 32 8 6 k 1 7 4 3 53 k 4 5 6 2 7 1 85 1 7 4 3 8 6 2 k4 7 k 1 2 5 3 8 66 3 2 8 q 4 5 7 18 5 1 3 7 6 2 k 4


7 3 5 1 4 2 N 6 8N 1 2 3 8 6 5 7 46 8 4 7 N 5 2 1 34 2 6 N 5 3 1 8 78 5 7 6 1 4 3 N 21 N 3 8 2 7 4 5 62 6 N 5 3 8 7 4 13 7 1 4 6 Q 8 2 55 4 8 2 7 1 6 3 N


1 7 6 3 Q 5 4 2 82 8 5 7 1 4 6 Q 3

Q 4 3 6 8 2 7 5 16 2 8 Q 5 3 1 7 44 1 7 8 2 6 Q 3 53 5 Q 1 4 7 8 6 28 3 4 2 6 Q 5 1 77 6 1 5 3 8 2 4 Q5 Q 2 4 7 1 3 8 6


8 5 2 3 N 6 7 1 41 3 7 8 2 4 5 6 N6 4 N 1 5 7 3 8 27 N 6 5 4 8 1 2 34 1 3 2 6 N 8 7 52 8 5 7 1 3 N 4 6N 7 8 6 3 2 4 5 15 2 4 N 7 1 6 3 83 6 1 4 8 5 2 N 7


6 4 3 8 2 7 5 1 Q

2 7 5 1 Q 6 3 8 4Q 8 1 5 4 3 2 7 63 6 7 2 8 1 4 Q 55 2 8 Q 3 4 1 6 71 Q 4 7 6 5 8 2 38 3 6 4 7 2 Q 5 17 5 Q 3 1 8 6 4 24 1 2 6 5 Q 7 3 8

236 Solutions

Solution for Puzzle #244:Q 7 1 4 3 6 8 5 2

6 8 2 7 Q 5 4 1 35 4 3 2 8 1 Q 6 73 6 5 1 7 8 2 4 Q1 2 7 Q 4 3 6 8 58 Q 4 5 6 2 7 3 14 1 6 3 2 7 5 Q 82 3 8 6 5 Q 1 7 47 5 Q 8 1 4 3 2 6


4 8 5 1 7 N 3 6 22 3 N 6 4 1 7 8 57 6 1 2 5 3 4 N 86 5 4 8 2 7 N 3 1N 1 8 7 6 2 5 4 38 2 3 N 1 5 6 7 45 4 7 3 N 8 1 2 63 7 6 5 8 4 2 1 N1 N 2 4 3 6 8 5 7


5 8 7 2 q 4 1 3 64 2 6 8 3 1 5 7 k1 3 k 5 6 7 8 2 46 1 8 3 5 2 q 4 72 k 5 7 4 6 3 1 87 4 3 k 1 8 6 5 2

q 6 1 4 2 3 7 8 58 5 2 1 7 q 4 6 33 7 4 6 8 5 2 k 1


4 5 6 1 3 8 2 k 7

q 7 1 2 6 5 3 8 48 3 2 7 4 q 1 5 67 2 3 k 8 6 4 1 51 k 8 4 5 2 7 6 35 6 4 3 7 1 8 2 k3 8 q 5 2 4 6 7 16 4 5 8 1 7 k 3 22 1 7 6 k 3 5 4 8


1 5 3 6 n 2 7 4 82 8 7 5 3 4 n 6 14 n 6 8 1 7 2 5 37 2 1 4 8 n 5 3 6n 6 8 7 5 3 4 1 23 4 5 2 6 1 8 n 75 3 2 n 7 6 1 8 48 1 4 3 2 5 6 7 n6 7 n 1 4 8 3 2 5


4 5 1 7 2 p 8 3 66 2 7 8 1 3 5 p 48 3 p 6 5 4 7 2 12 7 6 3 4 5 P 1 85 8 3 P 7 1 6 4 2P 1 4 2 6 8 3 5 73 p 2 1 8 7 4 6 57 6 5 4 3 2 1 8 P1 4 8 5 P 6 2 7 3

Solutions 237


2 6 8 3 1 4 7 5 n4 1 6 5 3 7 n 2 83 n 7 8 2 6 5 1 47 4 2 n 5 8 3 6 15 2 1 7 8 3 4 n 61 7 5 4 6 n 8 3 2n 8 3 6 7 2 1 4 58 5 n 2 4 1 6 7 36 3 4 1 n 5 2 8 7


1 3 4 5 N 8 6 2 72 6 8 3 7 1 5 N 45 N 7 2 6 4 8 3 13 4 6 1 8 N 7 5 28 2 1 7 5 6 3 4 N

N 7 5 4 3 2 1 8 67 8 2 N 1 5 4 6 36 1 N 8 4 3 2 7 54 5 3 6 2 7 N 1 8


8 4 3 2 n 1 5 6 72 6 5 3 8 7 n 4 1n 1 7 4 5 6 2 3 81 7 n 6 3 2 4 8 54 3 8 7 1 5 6 2 n6 5 2 8 4 n 1 7 33 8 1 5 6 4 7 n 27 n 6 1 2 3 8 5 45 2 4 n 7 8 3 1 6


6 8 4 7 5 k 3 1 25 3 7 2 8 1 4 q 61 2 q 4 3 6 7 8 54 7 6 8 k 3 5 2 1k 1 2 6 4 5 8 7 33 5 8 1 7 2 6 4 k2 4 5 q 6 7 1 3 87 6 1 3 2 8 q 5 48 k 3 5 1 4 2 6 7


3 5 1 2 6 8 N 7 44 7 6 5 3 N 2 1 88 N 2 4 1 7 3 5 67 3 N 1 4 2 6 8 56 8 4 7 5 3 1 2 N2 1 5 8 N 6 4 3 71 4 7 N 2 5 8 6 3N 6 8 3 7 1 5 4 25 2 3 6 8 4 7 N 1


1 7 6 2 3 5 N 4 83 5 4 8 6 N 1 2 72 8 N 1 7 4 5 6 37 4 2 5 8 3 6 N 16 3 5 7 N 1 2 8 48 N 1 6 4 2 3 7 54 2 7 3 1 6 8 5 Q5 1 8 N 2 7 4 3 6N 6 3 4 5 8 7 1 2

238 Solutions


3 5 8 7 2 4 1 6 N1 N 2 6 8 7 4 3 56 8 5 4 1 3 N 7 27 2 3 1 5 8 6 N 44 7 N 2 6 5 3 1 82 3 1 N 4 6 5 8 78 6 7 5 N 1 2 4 35 4 6 8 3 N 7 2 1N 1 4 3 7 2 8 5 6


3 2 5 8 4 6 Q 7 16 7 8 Q 1 5 3 4 21 Q 4 7 3 2 8 5 64 8 2 5 7 3 1 6 Q

7 6 1 4 2 Q 5 8 35 3 Q 6 8 1 4 2 78 1 7 2 Q 4 6 3 52 5 3 1 6 8 7 Q 4Q 4 6 3 5 7 2 1 8


5 7 3 1 4 2 6 8 Q8 6 2 7 Q 3 5 1 4Q 4 1 8 6 5 7 2 34 1 8 3 7 6 2 Q 56 3 5 Q 2 4 8 7 12 Q 7 5 1 8 4 3 67 5 4 2 3 1 Q 6 81 8 Q 6 5 7 3 4 23 2 6 4 8 Q 1 5 7


8 1 5 2 3 n 6 4 77 6 4 5 n 2 1 8 34 3 2 8 7 6 n 5 1n 2 8 1 6 5 3 7 46 5 3 n 4 1 7 2 81 n 6 7 2 4 8 3 53 7 1 4 5 8 2 6 n2 4 n 3 8 7 5 1 65 8 7 6 1 3 4 n 2


8 5 3 N 6 7 4 2 1N 4 6 1 8 2 7 3 51 2 7 4 3 5 N 6 85 7 4 3 1 8 2 N 63 N 1 2 5 6 8 4 72 6 8 7 N 4 1 5 34 8 5 6 7 N 3 1 26 1 2 8 4 3 5 7 N7 3 N 5 2 1 6 8 4


7 8 1 6 5 3 N 2 46 N 5 4 8 2 1 3 73 4 2 1 N 7 6 8 52 7 8 5 4 1 3 N 65 3 N 7 6 8 4 1 21 6 4 3 2 N 5 7 8N 5 3 8 7 4 2 6 14 1 7 2 3 6 8 5 Q8 2 6 N 1 5 7 4 3

Solutions 239


5 3 1 8 n 4 7 2 63 1 n 4 7 6 2 5 84 2 6 5 8 7 1 n 36 7 2 1 3 8 5 4 n2 8 7 6 4 1 n 3 5n 5 3 7 6 2 4 8 11 4 5 3 2 n 8 6 77 n 8 2 5 3 6 1 48 6 4 n 1 5 3 7 2


7 3 2 6 q 8 1 4 55 6 1 2 3 4 k 8 7k 4 8 7 5 1 3 6 22 1 k 3 6 7 4 5 83 8 6 4 1 5 2 7 k4 7 5 q 8 2 6 3 18 k 4 1 7 6 5 2 31 2 7 5 4 3 8 k 66 5 3 8 2 q 7 1 4


2 7 5 6 p 8 3 4 11 6 4 3 2 5 P 8 78 3 p 1 7 4 6 5 25 1 3 7 8 2 4 P 64 8 2 5 6 P 1 7 37 p 6 4 1 3 8 2 53 4 7 p 5 6 2 1 8p 2 1 8 3 7 5 6 46 5 8 2 4 1 7 3 P


3 7 2 6 5 q 8 1 41 5 8 3 4 2 7 k 64 q 6 1 7 8 2 3 57 8 1 4 2 3 5 6 k5 2 4 k 1 6 3 7 86 3 k 5 8 7 4 2 12 1 7 8 6 5 k 4 3

q 6 5 2 3 4 1 8 78 4 3 7 q 1 6 5 2


2 k 4 5 7 8 3 1 68 1 7 4 3 6 2 k 53 5 6 q 2 1 4 8 75 4 1 8 6 2 7 3 q

7 3 2 1 5 k 6 4 8k 6 8 7 4 3 1 5 24 7 3 6 8 5 k 2 16 8 k 2 1 4 5 7 31 2 5 3 q 7 8 6 4


8 2 4 6 1 7 3 Q 5

Q 5 7 2 4 3 6 8 16 3 1 5 Q 8 2 4 75 1 2 7 8 6 Q 3 47 Q 6 4 3 2 5 1 83 4 8 1 5 Q 7 6 22 6 Q 8 7 1 4 5 31 7 5 3 6 4 8 2 Q4 8 3 Q 2 5 1 7 6

240 Solutions


4 2 5 N 7 3 8 6 1N 8 3 4 6 1 5 2 77 1 6 8 2 5 4 3 N1 6 7 3 N 4 2 8 53 N 4 2 5 8 1 7 62 5 8 6 1 7 3 N 48 7 1 5 3 6 N 4 26 3 2 1 4 N 7 5 85 4 N 7 8 2 6 1 3


5 1 Q 2 7 4 8 6 37 3 6 5 8 1 4 Q 24 8 2 3 6 Q 7 1 56 7 1 Q 5 2 3 4 83 5 4 6 1 8 2 7 Q

Q 2 8 4 3 7 1 5 61 4 5 8 Q 3 6 2 72 6 3 7 4 5 Q 8 18 Q 7 1 2 6 5 3 4


N 3 8 1 6 4 7 2 54 6 2 7 3 5 1 8 N7 5 1 8 N 2 3 6 42 4 7 6 8 N 5 3 13 1 6 5 2 7 N 4 85 8 N 3 4 1 2 7 66 2 5 N 7 8 4 1 31 7 3 4 5 6 8 N 28 N 4 2 1 3 6 5 7


6 5 8 7 N 3 2 4 14 N 2 1 7 6 8 3 5N 8 3 5 2 1 4 7 68 2 6 4 3 N 1 5 77 3 1 2 8 4 5 6 N3 4 5 6 1 2 7 N 81 6 4 8 5 7 N 2 35 7 N 3 4 8 6 1 22 1 7 N 6 5 3 8 4


8 3 n 4 7 5 2 6 14 6 7 3 2 1 8 5 n1 2 5 n 8 6 3 7 45 8 4 1 3 2 6 n 72 7 1 6 n 4 5 8 36 n 3 7 5 8 4 1 23 1 2 5 6 7 n 4 8n 4 6 8 1 3 7 2 57 5 8 2 4 n 1 3 6


8 3 4 2 5 N 1 7 65 N 6 1 7 8 3 4 21 2 7 4 3 6 5 N 82 7 8 3 6 5 N 1 4N 4 1 7 8 2 6 3 53 6 5 N 4 1 8 2 77 8 2 6 N 3 4 5 14 5 3 8 1 7 2 6 N6 1 N 5 2 4 7 8 3

Solutions 241


4 8 2 5 3 N 7 1 65 7 6 1 2 4 N 8 33 1 N 7 8 6 4 5 28 6 3 N 4 2 1 7 5N 5 1 3 7 8 2 6 42 4 7 6 1 5 8 3 N7 3 5 4 Q 1 6 2 81 N 8 2 6 3 5 4 76 2 4 8 5 7 3 N 1


p 4 3 7 5 8 1 6 28 7 2 3 6 1 5 4 P5 6 1 P 2 4 8 3 76 3 5 1 7 P 4 2 81 8 7 2 4 5 6 p 34 2 P 8 3 6 7 1 57 1 4 5 P 2 3 8 62 5 6 4 8 3 p 7 13 P 8 6 1 7 2 5 4


1 7 8 2 6 n 3 4 56 n 5 3 7 4 1 2 82 3 4 1 8 5 n 7 6n 5 3 8 2 7 6 1 47 4 2 6 n 1 8 5 38 1 6 5 4 3 7 n 24 8 1 n 5 6 2 3 73 6 7 4 1 2 5 8 n5 2 n 7 3 8 4 6 1


7 6 8 4 2 1 N 5 34 3 N 1 7 5 8 6 21 N 5 7 6 4 3 2 85 2 6 8 N 3 7 1 48 7 3 2 4 6 1 N 56 4 7 3 1 2 5 8 N2 8 1 N 5 7 4 3 6N 5 4 6 3 8 2 7 13 1 2 5 8 N 6 4 7


8 2 6 1 7 3 N 5 47 4 5 N 6 8 3 1 2N 1 3 5 2 4 8 7 63 7 4 6 5 1 2 8 N5 6 N 7 8 2 1 4 31 8 2 3 4 N 5 6 76 5 1 2 N 7 4 3 82 3 8 4 1 6 7 N 54 N 7 8 3 5 6 2 1


1 4 5 7 3 Q 2 8 62 3 7 8 1 6 4 5 Q

Q 6 8 2 5 4 1 3 75 2 4 Q 7 8 3 6 18 7 3 6 4 1 Q 2 56 1 Q 3 2 5 7 4 84 5 2 1 8 7 6 Q 33 Q 1 5 6 2 8 7 47 8 6 4 Q 3 5 1 2

242 Solutions


8 5 2 7 4 1 3 N 63 4 6 8 N 5 7 2 17 N 1 6 3 2 5 4 85 6 3 4 7 8 N 1 22 7 8 3 1 N 4 6 5N 1 4 2 5 6 8 3 71 8 7 N 6 4 2 5 36 2 N 5 8 3 1 7 44 3 5 1 2 7 6 8 N


6 5 8 1 4 3 7 p 22 P 4 8 7 6 5 3 13 7 1 2 P 5 4 8 65 2 3 p 1 4 8 6 71 8 7 6 3 2 P 4 5P 4 6 5 8 7 1 2 34 6 2 7 5 8 3 1 p7 3 p 4 6 1 2 5 88 1 5 3 2 P 6 7 4


8 Q 5 2 3 1 6 4 71 3 6 7 4 8 2 5 Q2 4 7 5 6 Q 3 8 13 5 1 Q 2 6 4 7 87 8 4 3 1 5 Q 2 6Q 6 2 8 7 4 1 3 56 7 Q 4 8 2 5 1 35 2 3 1 Q 7 8 6 44 1 8 6 5 3 7 Q 2


1 4 8 6 2 n 7 5 3n 5 7 4 1 3 6 8 23 6 2 8 7 5 n 4 17 n 1 5 8 6 3 2 46 3 4 2 n 1 5 7 82 8 5 7 3 4 1 n 65 2 3 n 6 8 4 1 74 7 6 1 5 2 8 3 n8 1 n 3 4 7 2 6 5


1 Q 2 4 7 5 6 8 35 3 6 2 1 8 7 Q 44 7 8 3 Q 6 1 5 23 2 Q 6 5 4 8 7 18 4 5 7 2 1 3 6 Q7 6 1 8 3 Q 4 2 52 8 7 Q 4 3 5 1 6Q 5 3 1 6 7 2 4 86 1 4 5 8 2 Q 3 7


2 Q 6 4 5 8 1 3 77 3 8 2 6 1 Q 4 55 4 1 7 Q 3 6 8 23 8 2 6 1 5 7 Q 4

Q 1 4 3 8 7 2 5 66 7 5 Q 2 4 8 1 34 6 3 1 7 Q 5 2 88 2 Q 5 3 6 4 7 11 5 7 8 4 2 3 6 Q

Solutions 243


p 8 4 6 5 7 3 1 22 5 6 1 3 8 4 7 p3 1 7 p 4 2 6 5 86 2 5 8 7 P 1 4 31 3 P 4 6 5 2 8 74 7 8 2 1 3 5 p 68 p 3 5 2 4 7 6 17 4 1 3 p 6 8 2 55 6 2 7 8 1 P 3 4


2 7 4 8 6 3 1 5 n8 6 5 3 1 n 4 7 24 5 3 6 7 2 8 n 11 n 2 5 3 7 6 8 43 4 1 n 8 5 2 6 76 8 7 2 5 4 n 1 35 2 6 4 n 1 7 3 8n 1 8 7 2 6 3 4 57 3 n 1 4 8 5 2 6


5 6 n 8 7 3 1 2 42 1 7 6 n 4 5 8 34 8 3 2 5 1 n 6 77 3 4 n 6 8 2 1 56 n 1 5 4 2 3 7 88 5 2 3 1 7 6 4 n

n 4 5 7 2 6 8 3 11 2 8 4 3 5 7 n 63 7 6 1 8 n 4 5 2


5 4 8 2 1 3 N 7 66 3 N 1 7 8 5 2 47 6 5 N 3 2 4 8 1N 8 4 7 6 5 3 1 23 1 6 8 2 N 7 4 54 2 3 5 N 1 8 6 72 N 1 3 4 7 6 5 88 7 2 4 5 6 1 N 31 5 7 6 8 4 2 3 N


2 1 3 4 N 5 6 7 8N 6 4 1 8 7 2 3 57 5 8 2 6 3 N 1 41 3 N 6 5 2 4 8 78 2 7 N 3 4 1 5 66 4 5 8 7 1 3 N 25 7 2 3 1 6 8 4 N3 8 6 7 4 N 5 2 14 N 1 5 2 8 7 6 3


1 4 7 3 2 5 n 8 65 8 2 6 n 1 3 7 46 3 n 8 7 4 1 5 2n 6 5 4 8 3 7 2 18 1 4 2 5 7 6 3 n7 2 3 1 6 n 8 4 54 5 8 7 1 6 2 n 32 n 1 5 3 8 4 6 73 7 6 n 4 2 5 1 8

244 Solutions


Q 2 8 1 7 4 6 5 35 4 6 8 3 Q 7 1 27 3 1 5 2 6 8 Q 43 8 Q 6 1 2 5 4 74 6 7 3 5 8 Q 2 12 1 5 Q 4 7 3 8 61 Q 4 7 8 3 2 6 58 7 2 4 6 5 1 3 Q

6 5 3 2 Q 1 4 7 8


8 5 7 2 1 Q 4 6 34 2 Q 3 6 8 7 1 51 6 3 5 4 7 Q 2 83 Q 4 1 8 6 2 5 76 1 5 Q 7 2 8 3 42 7 8 4 3 5 1 Q 6Q 3 2 8 5 4 6 7 17 8 1 6 Q 3 5 4 25 4 6 7 2 1 3 8 Q


8 7 6 2 3 1 n 4 51 4 3 7 2 5 8 6 n5 8 n 6 7 4 3 1 2n 5 2 4 6 3 7 8 14 n 5 1 8 6 2 3 73 2 1 n 4 7 6 5 86 1 7 5 n 8 4 2 37 6 8 3 1 2 5 n 42 3 4 8 5 n 1 7 6


5 8 2 1 7 n 6 4 34 n 6 2 8 3 5 1 73 7 1 6 4 5 n 2 8n 2 5 7 3 1 8 6 46 4 3 5 n 8 2 7 17 1 8 4 6 2 3 n 58 3 7 n 1 6 4 5 22 6 4 8 5 7 1 3 n1 5 n 3 2 4 7 8 6


3 8 2 p 6 1 4 5 74 p 1 3 5 7 8 6 27 6 5 4 2 8 3 p 16 2 P 8 1 4 7 3 55 7 8 2 P 3 6 1 41 4 3 5 7 6 2 8 p2 3 4 1 8 p 5 7 6p 5 6 7 3 2 1 4 88 1 7 6 4 5 P 2 3


4 N 8 5 6 3 7 1 21 7 5 2 8 4 3 N 66 2 3 1 N 7 8 5 45 8 1 3 2 N 6 4 73 4 2 6 7 5 N 8 1N 6 7 4 1 8 2 3 57 5 4 N 3 2 1 6 82 1 N 8 4 6 5 7 38 3 6 7 5 1 4 2 N

Solutions 245


4 7 1 2 n 6 3 5 86 3 n 5 1 8 4 2 78 5 2 3 7 4 n 1 65 1 7 4 2 3 8 6 n

n 2 4 6 8 7 5 3 13 8 6 n 5 1 2 7 47 n 8 1 3 5 6 4 22 6 5 7 4 n 1 8 31 4 3 8 6 2 7 n 5


3 6 2 1 5 8 N 4 78 N 5 7 3 1 4 6 2N 8 1 5 7 4 6 2 37 4 6 N 2 5 3 1 82 7 4 8 6 3 1 N 54 5 3 6 1 2 8 7 N1 3 N 2 8 6 7 5 46 2 7 3 4 N 5 8 15 1 8 4 N 7 2 3 6


5 6 1 7 2 3 8 4 n

n 4 3 2 1 6 7 5 88 3 5 4 6 7 2 n 13 n 7 5 4 1 6 8 22 1 6 8 5 4 n 7 36 8 2 1 7 n 4 3 54 5 n 3 8 2 1 6 77 2 8 6 n 5 3 1 41 7 4 n 3 8 5 2 6


6 4 1 2 5 7 8 n 33 1 8 5 4 n 7 2 6n 7 5 4 6 3 2 8 17 6 2 n 1 8 5 3 42 n 6 8 3 1 4 5 71 8 7 3 2 6 n 4 54 5 3 6 8 2 1 7 n5 2 n 1 7 4 3 6 88 3 4 7 n 5 6 1 2


4 8 2 1 3 n 5 7 67 2 8 4 6 3 1 n 5n 1 4 5 7 6 8 2 33 7 n 6 5 4 2 8 15 3 1 8 n 7 4 6 26 n 3 2 1 5 7 4 82 5 7 n 8 1 6 3 41 4 6 7 2 8 3 5 n8 6 5 3 4 2 n 1 7


6 2 8 4 3 1 5 7 N4 5 1 3 7 8 6 N 23 6 N 5 1 2 7 4 81 3 6 7 8 N 2 5 48 7 4 2 N 3 1 6 52 4 5 N 6 7 8 1 37 1 3 8 4 5 N 2 6N 8 2 1 5 6 4 3 75 N 7 6 2 4 3 8 1

246 Solutions


4 7 6 5 1 N 3 2 82 8 5 6 7 3 N 1 43 1 N 2 8 4 5 6 71 4 8 N 6 2 7 3 56 5 2 3 4 7 1 8 Q

N 3 7 1 5 8 2 4 67 N 1 8 2 6 4 5 35 6 3 4 N 1 8 7 28 2 4 7 3 5 6 N 1


3 1 7 2 8 p 5 6 44 2 8 6 5 1 7 3 P5 6 P 7 4 3 1 8 2P 5 6 4 1 8 3 2 77 8 3 5 p 2 4 1 62 4 1 3 6 7 8 P 56 7 2 1 3 4 p 5 81 P 4 8 2 5 6 7 38 3 5 P 7 6 2 4 1


5 3 7 6 1 N 2 8 48 4 Q 5 2 7 3 1 61 2 6 3 8 4 5 7 N2 7 5 4 3 8 6 N 16 8 3 7 N 1 4 5 24 N 1 2 6 5 7 3 83 1 4 8 5 6 N 2 77 5 8 N 4 2 1 6 3N 6 2 1 7 3 8 4 5


2 p 1 6 7 3 5 8 47 3 5 2 4 8 6 p 16 4 8 1 5 P 3 2 7P 2 7 8 1 6 4 3 58 6 3 5 P 4 1 7 21 5 4 7 3 2 p 6 83 1 p 4 2 7 8 5 65 7 6 3 8 1 2 4 p4 8 2 P 6 5 7 1 3


7 1 5 6 4 3 p 8 2P 4 6 2 8 7 1 5 32 3 8 P 5 1 4 6 73 P 1 4 6 8 7 2 56 7 2 3 1 5 8 4 P5 8 4 7 2 p 3 1 64 2 p 8 3 6 5 7 18 5 7 1 P 2 6 3 41 6 3 5 7 4 2 P 8


7 1 2 4 5 6 3 p 83 6 8 2 p 1 7 4 54 5 P 3 8 7 6 2 12 7 5 1 4 P 8 3 66 3 1 7 2 8 4 5 p8 p 4 6 3 5 1 7 25 8 7 p 6 3 2 1 4P 2 3 8 1 4 5 6 71 4 6 5 7 2 P 8 3

Solutions 247


4 N 3 1 6 7 2 5 81 8 2 3 N 5 7 4 67 6 5 2 4 8 3 1 N3 2 N 5 8 1 6 7 46 5 7 4 2 N 8 3 18 1 4 7 3 6 N 2 55 4 8 6 7 2 1 N 3N 7 1 8 5 3 4 6 22 3 6 N 1 4 5 8 7


8 3 7 4 6 1 5 Q 24 1 5 7 Q 2 6 8 32 6 Q 8 3 5 7 4 1Q 7 4 3 8 6 1 2 53 2 8 1 5 4 Q 7 66 5 1 Q 2 7 4 3 85 8 3 6 4 Q 2 1 77 4 2 5 1 3 8 6 Q1 Q 6 2 7 8 3 5 4


7 8 4 5 3 1 N 2 63 2 5 4 6 N 1 7 8N 1 6 8 7 2 4 3 51 5 3 6 8 4 2 N 74 6 8 N 2 7 5 1 32 7 N 1 5 3 6 8 48 N 1 3 4 5 7 6 25 3 2 7 1 6 8 4 N6 4 7 2 N 8 3 5 1


4 1 2 3 6 5 8 7 p6 P 8 4 7 2 3 5 15 3 7 8 P 1 4 6 28 2 3 1 4 7 5 p 6P 7 6 5 2 8 1 4 31 4 5 p 3 6 7 2 87 6 1 2 5 3 P 8 43 5 P 6 8 4 2 1 72 8 4 7 1 P 6 3 5


2 7 4 8 5 3 6 n 11 3 5 2 n 6 7 4 88 6 7 4 1 2 5 3 n4 1 3 n 6 5 8 2 76 2 n 5 7 1 4 8 3n 4 1 6 3 8 2 7 55 8 2 7 4 n 3 1 67 n 6 3 8 4 1 5 23 5 8 1 2 7 n 6 4


5 p 8 2 6 4 3 1 73 6 1 8 P 7 4 5 27 2 4 3 1 5 6 8 p4 1 2 6 8 p 7 3 58 7 p 5 3 2 1 4 66 3 5 7 4 1 p 2 81 5 6 p 2 3 8 7 42 8 3 4 7 6 5 P 1P 4 7 1 5 8 2 6 3

248 Solutions


4 2 8 3 p 6 7 1 57 P 3 5 4 1 8 6 26 1 5 8 2 7 3 4 P

p 5 6 1 7 8 4 2 32 7 4 p 6 3 5 8 13 8 1 2 5 4 p 7 61 4 P 6 8 5 2 3 78 3 2 7 1 p 6 5 45 6 7 4 3 2 1 P 8


2 3 6 5 N 7 8 4 17 N 5 1 4 8 2 6 34 1 8 6 2 3 N 5 71 8 4 3 7 2 5 N 63 5 N 8 1 6 4 7 26 7 2 4 5 N 1 3 8N 6 3 2 8 5 7 1 45 2 1 7 3 4 6 8 N8 4 7 Q 6 1 3 2 5


2 1 8 3 n 5 6 7 47 6 5 2 4 1 n 3 8n 4 3 6 8 7 2 1 58 5 6 1 7 n 4 2 33 n 7 8 2 4 5 6 11 2 4 5 6 3 8 n 75 3 n 4 1 6 7 8 26 8 1 7 5 2 3 4 n4 7 2 n 3 8 1 5 6


3 7 5 n 4 1 8 2 64 1 6 5 2 8 3 7 n2 8 n 6 7 3 4 5 17 3 1 8 6 5 2 n 4n 6 4 2 3 7 1 8 58 5 2 4 1 n 7 6 36 n 7 1 8 4 5 3 21 2 3 7 5 6 n 4 85 4 8 3 n 2 6 1 7


3 4 1 Q 7 2 6 8 55 7 6 8 1 3 2 4 Q

2 8 Q 5 4 6 1 3 78 6 2 4 5 Q 7 1 31 Q 5 3 8 7 4 2 64 3 7 6 2 1 Q 5 86 1 3 2 Q 8 5 7 4Q 2 4 7 3 5 8 6 17 5 8 1 6 4 3 Q 2


p 7 8 1 3 6 2 5 46 5 2 7 4 8 3 1 p1 3 4 P 2 5 8 7 68 1 6 2 5 P 4 3 72 p 7 3 8 4 1 6 53 4 5 6 7 1 P 8 27 2 P 5 1 3 6 4 85 8 1 4 6 2 7 P 34 6 3 8 P 7 5 2 1

Solutions 249


7 8 3 N 1 5 6 2 42 4 1 3 6 8 N 7 55 N 6 4 7 2 8 1 31 6 N 7 8 3 5 4 28 7 2 1 5 4 3 N 63 5 4 2 N 6 7 8 14 3 7 5 2 N 1 6 8N 2 8 6 3 1 4 5 76 1 5 8 4 7 2 3 N


2 5 1 8 6 4 n 3 77 6 4 1 n 3 8 5 2n 3 8 5 2 7 6 1 43 1 5 7 8 n 4 2 66 n 7 4 3 2 1 8 54 8 2 6 5 1 3 7 n1 7 n 3 4 5 2 6 85 4 6 2 1 8 7 n 38 2 3 n 7 6 5 4 1


N 3 2 1 8 6 5 7 48 4 1 3 5 7 2 N 67 5 6 2 N 4 8 1 32 Q 8 6 3 1 4 5 75 1 3 4 7 8 N 6 24 6 7 5 2 N 1 3 81 7 5 8 6 2 3 4 N3 8 N 7 4 5 6 2 16 2 4 N 1 3 7 8 5


2 5 7 1 3 8 N 4 68 N 4 3 1 6 2 5 71 6 2 4 N 5 7 8 35 3 8 N 4 7 6 1 26 1 N 5 7 3 4 2 87 2 1 6 5 4 8 3 N3 4 6 7 8 2 1 N 5N 8 3 2 6 1 5 7 44 7 5 8 2 N 3 6 1


1 5 4 3 6 2 8 7 Q2 8 7 Q 4 5 6 3 13 Q 6 1 8 7 4 2 57 3 2 4 5 6 Q 1 88 4 Q 2 7 1 5 6 36 1 5 8 3 Q 2 4 74 7 1 5 2 8 3 Q 6Q 2 8 6 1 3 7 5 45 6 3 7 Q 4 1 8 2


3 1 n 8 5 4 6 7 24 8 6 2 n 3 7 1 57 5 2 n 1 8 4 6 36 7 4 3 8 n 5 2 15 2 7 6 3 1 n 8 41 6 5 7 4 2 8 3 n8 n 1 4 2 7 3 5 62 4 3 5 7 6 1 n 8n 3 8 1 6 5 2 4 7

250 Solutions


7 1 5 2 n 6 3 8 42 3 n 4 8 1 5 7 66 8 4 5 3 7 2 1 n3 6 2 7 4 8 n 5 15 n 7 1 2 3 4 6 81 4 8 n 6 5 7 2 3n 2 1 8 5 4 6 3 78 5 3 6 7 n 1 4 24 7 6 3 1 2 8 n 5


3 2 6 7 4 N 5 8 15 4 N 3 1 8 7 2 67 8 1 5 6 2 3 N 4N 1 8 6 7 4 2 5 36 5 3 2 N 1 8 4 72 7 4 8 3 5 1 6 N1 N 5 4 2 3 6 7 84 6 2 1 8 7 N 3 58 3 7 N 5 6 4 1 2


4 3 1 7 8 5 n 2 66 2 4 1 n 8 3 5 75 n 2 3 7 6 4 8 17 8 6 2 4 n 1 3 5n 6 5 8 1 2 7 4 31 4 7 5 2 3 6 n 82 5 3 n 6 1 8 7 43 7 8 6 5 4 2 1 n8 1 n 4 3 7 5 6 2


3 4 Q 7 5 8 1 2 68 6 2 1 4 Q 5 7 37 5 1 2 6 3 8 Q 44 1 6 8 Q 5 2 3 7Q 7 5 3 2 6 4 1 82 3 8 4 1 7 6 5 Q5 2 3 6 7 4 Q 8 16 Q 7 5 8 1 3 4 21 8 4 Q 3 2 7 6 5


6 Q 1 8 3 7 5 4 28 5 7 2 1 4 Q 3 62 4 3 5 Q 6 8 7 17 3 2 4 5 1 6 Q 8Q 1 6 3 7 8 4 2 54 8 5 Q 6 2 7 1 33 2 4 6 8 Q 1 5 71 6 Q 7 2 5 3 8 45 7 8 1 4 3 2 6 Q


3 6 8 2 7 4 5 n 18 4 2 n 1 3 7 5 62 7 5 3 6 1 8 4 n4 5 3 1 n 7 6 8 25 8 1 7 4 6 n 2 37 1 6 8 5 n 2 3 46 2 n 4 3 8 1 7 5n 3 7 6 2 5 4 1 81 n 4 5 8 2 3 6 7

Solutions 251


6 5 q 1 8 3 4 2 71 4 3 2 5 7 8 k 62 8 7 6 k 4 3 5 14 2 6 8 3 5 7 1 q

5 q 8 7 1 2 6 4 33 7 1 4 6 q 2 8 5k 1 2 3 7 8 5 6 47 6 4 5 2 1 k 3 88 3 5 k 4 6 1 7 2


6 3 5 2 4 1 N 7 81 N 3 6 5 2 8 4 72 4 N 7 6 8 3 5 13 5 6 1 2 4 7 8 N4 7 1 8 3 5 2 N 6N 2 7 4 8 3 1 6 58 1 2 5 7 N 6 3 45 6 8 3 N 7 4 1 27 8 4 N 1 6 5 2 3


3 6 2 n 8 1 4 7 58 4 5 7 3 6 1 2 n1 7 n 4 5 2 8 6 37 8 4 6 2 5 3 n 12 n 3 1 4 8 7 5 65 1 6 3 7 n 2 4 8n 3 8 2 6 7 5 1 46 5 7 8 1 4 n 3 24 2 1 5 n 3 6 8 7


3 N 4 1 6 7 8 2 55 1 8 2 N 3 4 7 67 6 2 4 5 8 3 N 1N 4 5 3 1 6 7 8 28 7 6 5 2 N 1 4 31 2 3 8 7 4 6 5 N4 3 N 6 8 2 5 1 76 5 7 N 4 1 2 3 82 8 1 7 3 5 N 6 4


6 2 7 n 5 1 4 3 88 n 4 7 3 2 6 1 55 3 1 8 4 6 7 2 n3 8 6 1 2 5 n 4 77 5 2 4 n 8 3 6 14 1 n 3 6 7 8 5 2n 6 5 2 8 4 1 7 32 7 3 6 1 n 5 8 41 4 8 5 7 3 2 n 6


5 7 1 k 2 3 8 4 62 q 3 4 8 6 1 5 78 4 6 1 5 7 3 2 k7 6 4 3 k 1 2 8 53 8 2 5 7 4 q 6 1

q 1 5 8 6 2 7 3 41 5 k 6 3 8 4 7 26 2 8 7 4 q 5 1 34 3 7 2 1 5 6 k 8

252 Solutions


6 5 7 1 8 2 3 Q 43 8 Q 4 7 5 6 1 24 1 2 6 Q 3 7 5 82 Q 8 7 5 6 4 3 11 7 6 2 3 4 5 8 Q5 4 3 8 1 Q 2 6 77 3 5 Q 4 8 1 2 68 2 1 5 6 7 Q 4 3Q 6 4 3 2 1 8 7 5


6 2 n 7 5 1 3 8 41 8 4 3 n 6 7 5 25 7 3 4 8 2 n 1 62 3 1 n 7 4 8 6 57 n 5 6 1 8 4 2 38 4 6 2 3 5 1 7 n

n 6 2 8 4 7 5 3 14 1 8 5 6 3 2 n 73 5 7 1 2 n 6 4 8


4 7 2 8 3 6 1 5 N5 3 N 4 2 1 6 8 78 1 6 N 5 7 2 4 33 6 8 5 1 2 N 7 47 4 5 6 8 N 3 1 22 Q 1 3 7 4 8 6 51 5 3 2 4 8 7 N 66 8 4 7 N 3 5 2 1N 2 7 1 6 5 4 3 8


1 6 3 8 7 k 5 4 22 4 5 3 6 1 k 7 8k 7 8 2 5 4 1 6 34 2 q 7 3 8 6 1 55 8 7 1 k 6 3 2 46 3 1 4 2 5 8 k 77 q 6 5 4 3 2 8 18 5 2 6 1 7 4 3 q

3 1 4 k 8 2 7 5 6


1 7 5 4 p 6 8 3 28 3 2 7 1 5 6 p 46 P 4 2 8 3 5 1 75 4 6 P 3 1 2 7 83 1 7 8 5 2 p 4 62 8 p 6 4 7 3 5 17 5 8 1 2 p 4 6 34 6 3 5 7 8 1 2 P

P 2 1 3 6 4 7 8 5


1 7 2 3 8 6 5 4 N6 Q 4 2 7 5 1 8 35 8 3 4 N 1 7 2 63 6 7 5 4 N 8 1 2N 4 8 1 2 7 3 6 52 5 1 8 6 3 4 N 77 3 6 N 1 4 2 5 88 1 N 7 5 2 6 3 44 2 5 6 3 8 N 7 1

Solutions 253


2 1 N 5 4 3 6 7 88 4 3 N 6 7 2 1 56 5 7 8 1 2 4 N 37 2 1 3 8 6 N 5 4N 8 4 7 2 5 1 3 63 6 5 4 N 1 8 2 74 3 8 2 7 N 5 6 15 N 6 1 3 8 7 4 21 7 2 6 5 4 3 8 N


8 5 4 2 N 7 6 3 16 7 2 8 1 3 4 N 5N 3 1 6 4 5 8 2 71 N 6 3 2 4 7 5 83 2 7 5 8 1 Q 6 44 8 5 N 7 6 2 1 35 4 N 7 3 2 1 8 67 6 8 1 5 N 3 4 22 1 3 4 6 8 5 7 N


1 6 3 2 4 N 7 8 58 5 N 3 2 7 1 4 62 3 6 5 7 4 8 1 N

N 4 1 7 5 8 6 2 37 2 4 N 8 6 5 3 16 7 5 4 1 3 2 N 84 1 7 8 3 5 N 6 25 N 8 1 6 2 3 7 43 8 2 6 N 1 4 5 7


3 5 1 8 4 7 2 6 Q

6 8 4 Q 2 3 5 7 12 Q 7 1 6 5 8 4 37 1 3 4 8 6 Q 2 55 4 Q 7 1 2 3 8 68 6 2 3 5 Q 7 1 41 3 5 2 7 4 6 Q 8Q 2 8 6 3 1 4 5 74 7 6 5 Q 8 1 3 2


3 6 7 5 8 N 4 1 2N 1 8 3 6 2 7 5 45 8 4 N 7 6 1 2 37 2 6 1 5 3 N 4 84 5 2 6 3 1 8 N 71 7 3 4 2 5 6 8 N2 3 1 8 N 4 5 7 68 N 5 2 4 7 3 6 16 4 N 7 1 8 2 3 5


3 1 4 6 q 8 2 7 5

q 7 8 2 5 4 3 1 66 5 2 1 3 7 k 8 42 6 k 5 1 3 8 4 77 3 1 4 8 k 5 6 28 4 5 7 2 6 1 3 q

1 8 6 q 7 5 4 2 35 2 7 3 4 1 6 k 84 k 3 8 6 2 7 5 1

254 Solutions


8 2 5 p 3 7 1 6 44 p 7 5 1 6 3 8 23 6 1 2 4 8 P 5 77 8 3 4 P 5 6 2 12 4 6 1 8 3 5 7 P5 1 p 6 7 2 4 3 81 7 2 3 5 4 8 P 6p 5 8 7 6 1 2 4 36 3 4 8 2 P 7 1 5


8 4 5 7 N 2 6 1 36 1 2 4 5 3 7 N 8N 7 3 8 6 1 4 5 23 N 7 6 2 4 1 8 54 5 8 1 3 Q 2 6 72 6 1 5 8 7 3 4 N5 2 N 3 4 6 8 7 17 3 6 N 1 8 5 2 41 8 4 2 7 5 N 3 6


5 6 1 3 8 p 4 7 2P 3 7 4 1 2 5 8 64 2 8 7 5 6 3 1 p1 P 3 6 7 4 2 5 87 5 2 8 P 1 6 4 38 4 6 2 3 5 1 p 72 8 P 1 4 3 7 6 53 7 4 5 6 8 p 2 16 1 5 P 2 7 8 3 4


7 1 3 2 6 4 N 5 84 N 8 3 5 1 7 2 66 2 5 8 N 7 1 4 32 4 7 N 1 3 6 8 58 6 N 5 7 2 4 3 13 5 1 6 4 8 2 N 71 8 4 7 2 5 3 6 N

N 3 2 1 8 6 5 7 45 7 6 4 3 N 8 1 2


1 Q 8 3 5 4 7 2 67 5 4 6 1 2 Q 3 82 6 3 8 Q 7 1 5 4

Q 8 1 4 3 5 2 6 75 3 6 2 7 1 4 8 Q4 2 7 Q 6 8 5 1 33 7 2 1 8 Q 6 4 56 4 5 7 2 3 8 Q 18 1 Q 5 4 6 3 7 2


3 4 2 5 8 7 N 1 67 8 N 2 4 3 6 5 15 2 8 1 3 6 7 4 N

N 1 6 3 7 5 4 8 24 3 1 N 6 2 5 7 86 5 3 7 N 1 8 2 41 6 5 8 2 4 3 N 72 N 7 4 5 8 1 6 38 7 4 6 1 N 2 3 5

Solutions 255


3 8 1 7 6 5 4 q 27 2 5 4 1 k 3 8 6k 4 6 2 3 8 1 7 56 5 q 8 4 7 2 1 32 1 4 3 k 6 7 5 88 3 7 5 2 1 k 6 41 7 3 6 8 4 5 2 q5 6 2 q 7 3 8 4 14 k 8 1 5 2 6 3 7


8 p 1 4 5 6 3 7 25 7 3 2 p 8 6 4 16 4 2 3 1 7 8 p 54 6 p 5 3 2 1 8 72 3 8 7 6 1 4 5 P1 5 7 P 8 4 2 6 33 1 4 8 7 P 5 2 67 2 6 1 4 5 p 3 8P 8 5 6 2 3 7 1 4


1 6 3 7 n 2 5 4 84 7 n 3 8 5 2 1 65 2 8 1 4 6 7 3 n7 5 4 8 2 1 n 6 38 n 2 6 5 3 1 7 43 1 6 n 7 4 8 5 2n 8 1 4 3 7 6 2 56 4 5 2 1 8 3 n 72 3 7 5 6 n 4 8 1


8 7 6 1 4 N 5 2 31 4 3 5 7 2 6 8 N

N 2 5 6 3 8 7 4 13 8 4 2 6 7 N 1 52 1 7 N 5 4 3 6 86 5 N 3 8 1 4 7 27 N 2 4 1 3 8 5 65 3 8 7 2 6 1 N 44 6 1 8 N 5 2 3 7


2 4 5 8 6 1 7 k 36 3 k 2 7 4 8 1 57 8 1 k 5 3 4 6 2

q 7 3 4 8 2 6 5 15 1 8 3 k 6 2 4 74 2 6 5 1 7 q 3 81 q 7 6 3 8 5 2 43 6 2 7 4 5 1 8 k8 5 4 1 2 k 3 7 6


4 8 n 5 2 6 7 1 36 1 2 3 7 4 5 8 n7 3 5 n 1 8 4 2 63 4 6 7 5 2 8 n 15 2 1 8 n 3 6 4 7n 7 8 6 4 1 2 3 52 5 4 1 3 7 n 6 88 n 3 2 6 5 1 7 41 6 7 4 8 n 3 5 2

256 Solutions


1 5 6 4 3 8 k 2 7k 8 7 5 2 1 3 6 44 2 3 7 6 q 8 1 57 4 2 k 1 5 6 8 38 k 1 3 4 6 5 7 26 3 5 2 8 7 1 4 k5 6 k 8 7 4 2 3 12 1 4 6 q 3 7 5 83 7 8 1 5 2 4 q 6


8 N 7 5 2 3 1 4 63 5 6 7 4 1 2 8 N2 1 4 6 N 8 5 7 34 2 8 N 7 5 3 6 16 7 N 1 3 4 8 2 55 3 1 8 6 2 4 N 77 8 3 2 1 6 N 5 41 6 2 4 5 N 7 3 8Q 4 5 3 8 7 6 1 2


1 8 2 k 6 3 5 4 77 q 6 4 5 1 2 3 83 5 4 2 7 8 1 6 k6 2 5 7 k 4 8 1 34 3 7 1 8 6 q 2 5

q 1 8 5 3 2 6 7 45 4 k 6 2 7 3 8 18 6 1 3 4 k 7 5 22 7 3 8 1 5 4 q 6


8 6 2 q 5 3 1 4 74 7 5 1 2 8 3 6 q

3 1 k 6 7 4 8 5 27 2 4 3 8 1 5 k 65 3 6 7 4 k 2 8 1

q 8 1 5 6 2 4 7 31 5 3 4 k 7 6 2 86 k 8 2 3 5 7 1 42 4 7 8 1 6 q 3 5


2 8 7 4 1 k 6 5 36 k 5 7 3 2 1 8 43 4 1 5 6 8 q 2 7

q 3 2 8 7 5 4 6 11 7 8 k 4 6 2 3 55 6 4 1 2 3 7 q 88 1 6 3 q 7 5 4 24 2 3 6 5 1 8 7 k7 5 k 2 8 4 3 1 6


1 6 4 2 N 5 8 3 72 N 7 3 4 8 1 6 53 5 8 7 6 1 4 N 28 3 6 4 1 2 5 7 N7 1 N 5 8 6 3 2 44 2 5 N 7 3 6 1 8N 8 2 1 3 4 7 5 66 7 3 8 5 N 2 4 15 4 1 6 2 7 N 8 3

Solutions 257


5 1 4 7 Q 3 8 2 6Q 8 3 2 6 5 4 1 77 6 2 4 8 1 5 Q 32 4 8 6 5 Q 3 7 16 7 Q 1 3 4 2 5 81 3 5 8 2 7 Q 6 48 Q 7 5 4 6 1 3 23 2 1 Q 7 8 6 4 54 5 6 3 1 2 7 8 Q


6 N 3 2 7 8 5 1 45 4 8 1 3 N 2 6 78 1 7 6 4 2 N 5 31 6 4 7 2 3 8 N 5N 3 2 5 8 6 4 7 12 7 5 3 N 1 6 4 83 5 1 N 6 4 7 8 27 8 N 4 1 5 3 2 64 2 6 8 5 7 1 3 N


7 5 N 8 3 6 1 2 46 8 2 1 5 4 7 3 N3 1 4 7 N 2 5 8 68 2 7 3 6 N 4 1 55 N 6 2 4 1 8 7 31 4 3 5 8 7 6 N 22 6 8 4 7 3 N 5 1N 7 1 6 2 5 3 4 84 3 5 N 1 8 2 6 7


N 1 8 7 5 3 2 6 43 7 6 1 2 4 N 5 82 4 5 N 6 8 7 1 31 5 2 4 N 7 8 3 64 6 7 8 3 2 5 N 18 3 N 6 1 5 4 2 77 N 3 2 8 6 1 4 55 8 1 3 4 Q 6 7 26 2 4 5 7 1 3 8 N


6 2 1 Q 3 7 4 8 58 7 3 5 4 2 N 6 1N 4 5 8 1 6 2 3 75 1 7 6 8 4 3 2 N3 8 4 2 5 N 7 1 62 6 N 3 7 1 5 4 84 5 2 7 6 8 1 N 31 3 6 4 N 5 8 7 27 N 8 1 2 3 6 5 4


8 6 4 Q 2 1 3 7 55 1 7 6 8 3 Q 2 43 2 Q 4 7 5 6 8 11 4 5 3 6 8 2 Q 77 Q 8 5 4 2 1 3 66 3 2 1 Q 7 4 5 82 8 3 7 1 6 5 4 Q4 7 1 2 5 Q 8 6 3

Q 5 6 8 3 4 7 1 2

258 Solutions


1 4 8 2 6 5 N 3 72 5 6 N 7 3 8 1 43 7 N 8 4 1 5 6 28 2 3 6 1 4 7 5 N4 1 7 5 3 Q 6 2 86 N 5 7 8 2 1 4 3N 6 2 3 5 8 4 7 15 3 4 1 N 7 2 8 67 8 1 4 2 6 3 N 5


8 1 2 5 7 3 n 4 6n 7 5 4 2 6 1 3 86 4 3 1 8 n 5 7 22 n 8 3 5 4 7 6 11 3 6 2 n 7 4 8 57 5 4 6 1 8 3 2 n4 2 n 7 6 5 8 1 35 6 7 8 3 1 2 n 43 8 1 n 4 2 6 5 7


3 7 n 4 2 1 6 5 88 2 1 5 3 6 4 7 n4 5 6 n 8 7 1 2 36 1 2 8 7 5 3 n 45 8 3 6 n 4 7 1 2n 4 7 2 1 3 8 6 51 6 8 3 5 2 n 4 77 n 5 1 4 8 2 3 62 3 4 7 6 n 5 8 1


4 6 3 5 8 1 k 7 28 1 2 3 q 7 5 4 6

q 5 7 6 4 2 1 3 81 4 8 2 5 3 7 6 k5 3 k 7 6 4 8 2 12 7 6 8 1 k 4 5 36 2 5 1 7 8 3 q 43 k 1 4 2 5 6 8 77 8 4 q 3 6 2 1 5


3 6 7 N 8 5 4 1 28 4 6 1 N 3 2 7 57 3 5 2 6 1 8 4 N4 2 N 5 3 7 1 6 81 5 8 4 2 6 N 3 72 8 1 6 5 4 7 N 35 N 4 7 1 8 3 2 6N 7 3 8 4 2 6 5 16 1 2 3 7 N 5 8 4


2 3 7 6 n 4 1 5 85 8 4 2 1 7 n 3 66 1 n 3 8 5 7 4 2n 7 3 8 2 6 4 1 54 6 8 1 5 3 2 7 n1 2 5 4 7 n 6 8 33 5 2 7 6 1 8 n 47 4 6 n 3 8 5 2 18 n 1 5 4 2 3 6 7

Solutions 259


2 5 7 4 8 q 6 3 13 6 4 5 1 2 7 k 88 1 q 3 6 7 2 4 57 3 8 1 k 5 4 2 6k 2 5 6 4 3 1 8 71 4 6 7 2 8 3 5 k4 k 3 8 7 1 5 6 25 8 1 2 3 6 q 7 46 7 2 q 5 4 8 1 3


4 1 n 6 3 8 5 7 28 7 3 1 2 5 4 6 n2 5 6 n 7 4 3 1 86 2 5 3 4 1 8 n 7n 3 4 2 8 7 1 5 61 8 7 5 6 n 2 4 33 n 2 4 5 6 7 8 15 6 8 7 1 2 n 3 47 4 1 8 n 3 6 2 5


1 4 7 3 6 N 5 8 22 5 6 8 7 4 N 1 3Q 8 3 5 1 2 4 7 67 6 8 N 4 3 2 5 13 2 4 1 5 7 6 N 85 N 1 2 8 6 3 4 76 7 N 4 3 1 8 2 54 3 5 7 2 8 1 6 N8 1 2 6 N 5 7 3 4


6 8 2 3 5 k 1 7 47 3 q 8 1 4 2 5 61 5 4 2 6 7 3 k 83 1 7 k 4 2 8 6 52 6 8 1 7 5 4 3 q

q 4 5 6 3 8 7 1 24 2 1 7 q 6 5 8 35 k 3 4 8 1 6 2 78 7 6 5 2 3 k 4 1


8 3 4 q 5 1 6 7 27 k 1 2 6 3 8 5 46 2 5 7 4 8 q 3 15 1 8 6 k 4 3 2 72 6 3 8 7 5 1 4 k

k 4 7 3 1 2 5 6 83 7 6 1 2 q 4 8 54 8 q 5 3 7 2 1 61 5 2 4 8 6 7 k 3


N 4 3 6 7 8 5 1 28 1 5 2 N 3 7 6 47 6 2 4 5 1 8 N 36 8 4 1 3 2 N 7 55 3 1 7 4 N 6 2 82 N 7 5 8 6 4 3 13 7 6 8 2 5 1 4 Q4 2 8 N 1 7 3 5 61 5 N 3 6 4 2 8 7

260 Solutions


8 k 6 7 2 1 5 3 47 5 4 3 8 6 1 2 k1 2 3 q 5 4 7 6 82 3 8 4 7 5 q 1 6

q 6 7 8 1 3 2 4 55 4 1 6 k 2 8 7 34 7 k 1 3 8 6 5 26 8 2 5 4 7 3 q 13 1 5 2 6 k 4 8 7


5 2 1 N 7 4 3 6 86 1 N 5 8 3 7 2 43 8 5 6 4 2 N 1 78 3 4 7 2 1 6 N 54 6 2 3 1 7 5 8 N2 5 7 8 N 6 4 3 11 7 3 4 6 N 8 5 27 N 6 2 5 8 1 4 3N 4 8 1 3 5 2 7 6


6 7 4 N 1 8 2 5 3N 1 5 6 3 2 8 7 48 3 2 5 4 7 N 1 65 6 1 3 8 N 4 2 72 8 Q 4 7 6 5 3 13 4 7 2 5 1 6 8 N7 5 8 1 6 4 3 N 21 2 6 8 N 3 7 4 54 N 3 7 2 5 1 6 8


1 n 3 6 5 7 4 8 27 5 2 n 8 4 3 6 14 6 8 3 1 2 5 7 n5 3 1 2 7 6 n 4 88 2 7 4 n 1 6 3 56 4 n 5 3 8 1 2 7n 7 6 1 2 3 8 5 42 1 4 8 6 5 7 n 33 8 5 7 4 n 2 1 6


5 4 6 8 7 1 q 3 2

q 8 7 3 2 5 4 1 63 2 1 q 6 4 8 5 74 5 8 2 1 7 6 k 37 6 3 5 k 8 2 4 11 k 2 4 3 6 7 8 52 7 5 1 4 k 3 6 88 3 4 6 5 2 1 7 k6 1 q 7 8 3 5 2 4


N 2 7 5 1 4 6 8 34 6 3 2 N 8 1 7 51 8 5 3 6 7 4 N 25 4 N 1 7 6 3 2 82 3 1 N 8 5 7 6 48 7 6 4 2 3 5 1 N3 1 8 6 5 N 2 4 77 5 2 8 4 1 N 3 66 N 4 7 3 2 8 5 1

Solutions 261


1 4 6 8 3 2 k 5 78 3 q 1 7 5 4 6 25 7 2 4 6 k 1 8 36 2 8 5 1 4 7 3 q

4 5 1 3 q 7 6 2 87 q 3 2 8 6 5 4 12 1 5 7 4 3 8 k 6k 8 4 6 2 1 3 7 53 6 7 k 5 8 2 1 4


4 2 6 N 1 8 3 7 58 3 1 5 2 7 6 N 47 N 5 4 3 6 2 1 83 1 8 7 5 N 4 2 65 6 2 3 4 1 N 8 7N 7 4 8 6 2 1 5 36 8 7 1 N 4 5 3 21 4 3 2 7 5 8 6 Q2 5 N 6 8 3 7 4 1


6 1 2 3 8 5 7 4 n3 7 5 6 1 4 n 2 87 4 n 5 3 6 2 8 18 6 3 n 4 2 1 7 54 n 8 2 5 7 6 1 35 2 1 8 n 3 4 6 7n 3 4 7 6 1 8 5 21 8 7 4 2 n 5 3 62 5 6 1 7 8 3 n 4


2 N 1 8 4 6 3 7 57 6 5 3 1 2 N 8 43 4 8 N 5 7 2 1 64 8 6 2 N 3 7 5 1N 2 7 5 6 1 4 3 85 1 3 7 8 4 6 2 Q8 5 2 4 3 N 1 6 76 3 N 1 7 8 5 4 21 7 4 6 2 5 8 N 3


3 2 8 6 7 4 N 1 58 5 7 N 3 1 6 2 41 4 N 5 6 8 2 3 76 1 2 4 8 N 7 5 37 3 1 2 N 5 4 6 84 7 3 8 5 2 1 N 62 6 4 3 1 7 5 8 N5 N 6 1 4 3 8 7 2N 8 5 7 2 6 3 4 1


1 7 6 5 4 q 3 8 23 4 2 8 7 1 6 k 58 q 5 6 3 2 1 4 74 6 7 3 2 5 8 1 k2 3 1 k 6 8 7 5 4k 5 8 4 1 7 2 6 35 2 3 1 8 4 k 7 66 8 k 7 5 3 4 2 17 1 4 2 q 6 5 3 8

262 Solutions


4 2 8 6 5 3 Q 1 76 5 7 Q 1 8 2 3 43 Q 1 7 4 2 6 5 81 7 6 2 Q 5 4 8 35 3 2 4 8 6 7 Q 1Q 8 4 1 3 7 5 2 67 6 Q 8 2 1 3 4 58 4 3 5 7 Q 1 6 22 1 5 3 6 4 8 7 Q


2 6 5 1 4 n 7 8 34 5 1 n 7 8 3 2 65 1 7 8 6 2 n 3 41 7 n 3 5 4 8 6 28 3 4 6 n 7 2 5 17 n 8 2 3 6 4 1 53 2 6 4 8 5 1 n 7n 4 3 5 2 1 6 7 86 8 2 7 1 3 5 4 n


3 5 1 6 8 4 2 N 74 8 2 7 N 6 1 3 56 N 8 2 3 7 5 1 4N 1 6 5 7 3 4 2 81 7 5 N 4 2 8 6 35 2 3 4 1 8 6 7 N2 4 7 8 6 N 3 5 17 3 4 1 2 5 N 8 68 6 N 3 5 1 7 4 2


7 8 1 6 4 5 2 n 32 4 6 1 3 n 7 8 53 5 n 7 2 4 8 1 61 6 2 8 n 3 5 7 44 n 5 3 8 7 1 6 25 2 3 n 7 1 6 4 8n 7 8 5 6 2 4 3 16 3 4 2 1 8 n 5 78 1 7 4 5 6 3 2 n


2 4 5 8 7 N 6 3 17 8 1 6 2 3 N 4 53 6 N 1 5 4 7 2 86 5 2 3 8 1 4 7 N4 1 3 7 N 2 5 8 68 N 7 4 6 5 2 1 35 3 6 2 4 8 1 Q 71 7 4 N 3 6 8 5 2N 2 8 5 1 7 3 6 4


N 1 3 5 7 6 2 8 46 3 1 7 4 8 5 2 N5 6 2 3 N 1 7 4 87 2 4 N 8 5 3 1 62 4 8 1 3 7 6 N 51 N 5 8 6 2 4 7 38 5 N 6 2 4 1 3 74 8 7 2 5 3 N 6 13 7 6 4 1 N 8 5 2

Solutions 263


7 2 3 1 4 N 8 6 56 4 N 5 3 8 1 2 75 1 8 7 6 2 4 N 33 6 2 4 8 1 7 5 N1 7 4 2 N 5 3 8 68 N 5 6 7 3 2 4 1N 8 1 3 5 4 6 7 24 3 7 N 2 6 5 1 82 5 6 8 1 7 N 3 4


2 Q 5 7 4 8 6 1 34 1 3 6 5 Q 2 7 87 6 8 2 3 1 5 4 Q8 4 Q 3 7 6 1 5 26 5 1 8 Q 2 4 3 73 2 7 4 1 5 8 Q 65 3 2 Q 6 4 7 8 1Q 8 4 1 2 7 3 6 51 7 6 5 8 3 Q 2 4


5 4 8 p 6 1 7 3 26 1 7 2 3 5 4 p 83 p 2 4 7 8 1 6 57 2 3 6 5 4 P 8 11 8 5 3 P 2 6 7 44 6 p 1 8 7 2 5 3P 7 1 5 4 3 8 2 62 3 6 8 1 P 5 4 78 5 4 7 2 6 3 1 P


3 8 4 n 7 6 2 5 15 n 6 4 1 2 3 8 77 2 1 8 5 3 4 6 n6 1 2 5 4 n 7 3 88 4 3 7 2 1 6 n 5n 5 7 6 3 8 1 4 21 7 n 3 6 5 8 2 44 3 8 2 n 7 5 1 62 6 5 1 8 4 n 7 3


5 q 4 7 3 1 8 2 62 6 3 k 8 5 1 4 77 8 1 2 4 6 3 5 k3 5 2 4 6 7 q 8 18 4 7 1 k 3 5 6 26 1 k 5 2 8 7 3 4

q 3 8 6 7 4 2 1 54 2 5 3 1 k 6 7 81 7 6 8 5 2 4 q 3


7 k 6 3 4 2 8 5 11 8 4 7 5 6 2 3 k3 2 5 q 1 8 7 6 4k 1 2 4 7 5 6 8 34 7 3 8 6 1 k 2 56 5 8 2 q 3 4 1 72 3 k 5 8 4 1 7 65 4 1 6 2 7 3 k 88 6 7 1 3 q 5 4 2

264 Solutions


7 4 Q 8 3 2 1 6 52 5 8 6 7 1 4 3 N1 6 3 4 5 N 2 7 86 8 7 3 N 4 5 2 14 N 1 7 2 5 6 8 33 2 5 1 8 6 N 4 75 3 2 N 4 8 7 1 6N 7 6 2 1 3 8 5 48 1 4 5 6 7 3 N 2


2 1 6 3 N 7 8 4 55 4 3 6 8 2 1 N 7N 7 8 5 1 4 2 3 68 2 4 7 5 N 3 6 13 6 1 4 2 8 7 5 N7 5 N 1 3 6 4 8 21 8 2 N 4 5 6 7 36 3 5 8 7 1 N 2 44 N 7 2 6 3 5 1 8

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