Solucion Reto 1 Los cuatro 4 - SOS ProfesSolucion Reto 1 Los cuatro 4.indd Created Date 8/28/2016...
1
Posibles soluciones: 0 = 4 – 4 + 4 – 4 1 = 4/4 + 4 – 4 2 = (4/4) + (4/4) 3 = ((4*4) – 4)/4 4 = 4*(4 – 4) + 4 5 = sqrt(4)+sqrt(4)+4/4 6 = sqrt(4)*(4-4/4) 7 = 4 + 4 – 4/4 8 = 4*sqrt(4) + 4 – 4 9 = (4-4/4)^sqrt(4) 10 = 4*sqrt(4) + 4/sqrt(4) 11 = 44/(sqrt(4)*sqrt(4)) 12 = (Sqrt(4) + Sqrt(4) + Sqrt(4))*Sqrt(4) 13 = 44/4 + sqrt(4) 14 = 4*4 – 4/sqrt(4) 15 = 44/4 + 4 16 = sqrt(4)*sqrt(4)*sqrt(4)*sqrt(4) 17 = 4*4+4/4 18 = 44/sqrt(4)-4 19 = 4! – 4 – 4/4 20 = (4/4+4)*4 21 = 4! – 4/4 – sqrt(4) 22 = 4*4 + 4 + sqrt(4) 23 = 4! – sqrt(4)*sqrt(4)/4 24 = 4! + 4 – sqrt(4) – sqrt(4) 25 = 4! + sqrt(4)*sqrt(4)/4 26 = 4! + sqrt(4)*sqrt(4)/sqrt(4) 27 = 4! + 4/4 + sqrt(4) 28 = 4! + 4*4/4 29 = 4! + 4 + 4/4 30 = ((4+4/4)!)/4 31 = ((4! + 4) / 4) + 4! 32 = 4^sqrt(4)+4^sqrt(4) 33 = 44/(sqrt(.4…)*sqrt(4)) 34 = ((4·4)·Sqrt(4)) + Sqrt(4) 35 = (4!) + (44/4) 36 = (4!*4!)/(4*4) 37 = ( 4! + Sqrt(4) ) / Sqrt(.4) – Sqrt(4) 38 = 44 – (4 + Sqrt(4)) 39 = ( 4! + 4 – Sqrt(4) ) / Sqrt(.4) 40 = (4!) + (4!) – 4 – 4 41 = ( 4! + Sqrt(4) ) / Sqrt(.4) + Sqrt(4) 42 = 44 – (4/Sqrt(4)) 43 = 44 – (4/4) 44 = 44 + 4 -4 45 = 44 + (4/4) 46 = ((4!)·4 – 4)/Sqrt(4) 47 = ((4!)·4 – Sqrt(4))/Sqrt(4) 48 = (4!)·Sqrt(4) + 4 – 4 49 = 4! * sqrt(4) + 4/4 50 = (4!)·Sqrt(4) + 4 – Sqrt(4) 51 = (4!/.4) – Sqrt(4/.4) 52 = (4!)·Sqrt(4) + Sqrt(4) + Sqrt(4) 53 = (4!/,4…) – 4/4 54 = (4!/,4…) + 4 – 4 55 = (4!/,4…) + 4/4 56 = 4! * sqrt(4) + 4 + 4 57 = (4!/,4…) + Sqrt(4/,4…) 58 = (4!/,4) – 4/Sqrt(4) 59 = (4!/,4…) + Sqrt(4)/,4 60 = (4!/,4…) + 4/Sqrt(,4…) 61 = (4!/,4) + 4/4 62 = (4!/,4…) + 4 + 4 63 = (4^4-4)/4 64 = 4! * sqrt(4) + 4 * 4 65 = (4!/,4) + Sqrt(4)/,4 66 = (4!/,4…) + 4!/Sqrt(4) 67 = ((4! + 4)/,4…) + 4 68 = (4!/,4) + 4 + 4 69 = (4!/,4) + 4/,4… 70 = (4!/,4…) + 4*4 71 = (4!+4.4)/.4 72 = (4!*4!)/(sqrt(4)*4) 73 = (4! + 4! + Sqrt(,4…))/Sqrt(,4…) 74 = 4!+4!+4!+sqrt(4) 75 = (4!+4!/4)/.4 76 = 4!+4!+4!+4 77 = (4/.4…)^sqrt(4)-4 78 = (4!-4)·4-Sqrt(4) 79 = (4/.4…)^sqrt(4)-sqrt(4) 80 = ((4^sqrt(4))/,4) * sqrt(4) 81 = (4-4/4)^4 82 = (4!-4)·4+ sqrt(4) 83 = (4/.4…)^sqrt(4)+sqrt(4) 84 = 44·Sqrt(4)-4 85=(4/.4…)^sqrt(4)+4 86 = 44/.4-4! 87 = (4! * 4) – (4/,4…) 88 = (4^4)/4 + 4! 89 = (sqrt(4)+4!)/.4+4! 90 = (4 + Sqrt(4))! / (4·Sqrt(4)) 91 = (4! * 4) – (sqrt(4)/,4) 92 = 44 + 4! + 4! 93 = 4!·4-sqrt(4/.4…) 94 = (4!)*4 – 4 + Sqrt(4) 95 = 4*4!-4/4 96 = 4 * 4! + 4 – 4 97 = 4 * 4! + 4/4 98 = 4! * 4 + 4 – Sqrt(4) 99 = ((4! – Sqrt(4)) * Sqrt(4) ) / .4… 100 = 4! * 4 + Sqrt(4) * Sqrt(4) Como véis muchos de estos números se consiguen con contenidos matemáticos que el alumnado de primaria aún no ha estudiado, por lo que el objetivo puede ser cuántos números se han conseguido de media y distintas formas de obtener un mismo número. Recuerda: ¡Lo importante es participar y fomentar la creatividad¡
Transcript of Solucion Reto 1 Los cuatro 4 - SOS ProfesSolucion Reto 1 Los cuatro 4.indd Created Date 8/28/2016...
Posibles soluciones:0 = 4 – 4 + 4 – 41 = 4/4 + 4 – 42 = (4/4) + (4/4)3 = ((4*4) – 4)/44 = 4*(4 – 4) + 45 = sqrt(4)+sqrt(4)+4/46 = sqrt(4)*(4-4/4)7 = 4 + 4 – 4/48 = 4*sqrt(4) + 4 – 49 = (4-4/4)^sqrt(4)10 = 4*sqrt(4) + 4/sqrt(4)11 = 44/(sqrt(4)*sqrt(4))12 = (Sqrt(4) + Sqrt(4) + Sqrt(4))*Sqrt(4)13 = 44/4 + sqrt(4)14 = 4*4 – 4/sqrt(4)15 = 44/4 + 416 = sqrt(4)*sqrt(4)*sqrt(4)*sqrt(4)17 = 4*4+4/4 18 = 44/sqrt(4)-419 = 4! – 4 – 4/420 = (4/4+4)*4 21 = 4! – 4/4 – sqrt(4) 22 = 4*4 + 4 + sqrt(4)23 = 4! – sqrt(4)*sqrt(4)/424 = 4! + 4 – sqrt(4) – sqrt(4)25 = 4! + sqrt(4)*sqrt(4)/426 = 4! + sqrt(4)*sqrt(4)/sqrt(4)27 = 4! + 4/4 + sqrt(4)28 = 4! + 4*4/429 = 4! + 4 + 4/430 = ((4+4/4)!)/431 = ((4! + 4) / 4) + 4!32 = 4^sqrt(4)+4^sqrt(4)33 = 44/(sqrt(.4…)*sqrt(4))34 = ((4·4)·Sqrt(4)) + Sqrt(4)35 = (4!) + (44/4)36 = (4!*4!)/(4*4)37 = ( 4! + Sqrt(4) ) / Sqrt(.4) – Sqrt(4)
38 = 44 – (4 + Sqrt(4))39 = ( 4! + 4 – Sqrt(4) ) / Sqrt(.4)40 = (4!) + (4!) – 4 – 441 = ( 4! + Sqrt(4) ) / Sqrt(.4) + Sqrt(4)42 = 44 – (4/Sqrt(4))43 = 44 – (4/4)44 = 44 + 4 -445 = 44 + (4/4) 46 = ((4!)·4 – 4)/Sqrt(4)47 = ((4!)·4 – Sqrt(4))/Sqrt(4)48 = (4!)·Sqrt(4) + 4 – 449 = 4! * sqrt(4) + 4/450 = (4!)·Sqrt(4) + 4 – Sqrt(4)51 = (4!/.4) – Sqrt(4/.4)52 = (4!)·Sqrt(4) + Sqrt(4) + Sqrt(4)53 = (4!/,4…) – 4/454 = (4!/,4…) + 4 – 455 = (4!/,4…) + 4/456 = 4! * sqrt(4) + 4 + 457 = (4!/,4…) + Sqrt(4/,4…)58 = (4!/,4) – 4/Sqrt(4)59 = (4!/,4…) + Sqrt(4)/,460 = (4!/,4…) + 4/Sqrt(,4…)61 = (4!/,4) + 4/462 = (4!/,4…) + 4 + 463 = (4^4-4)/464 = 4! * sqrt(4) + 4 * 465 = (4!/,4) + Sqrt(4)/,466 = (4!/,4…) + 4!/Sqrt(4)67 = ((4! + 4)/,4…) + 468 = (4!/,4) + 4 + 469 = (4!/,4) + 4/,4… 70 = (4!/,4…) + 4*471 = (4!+4.4)/.472 = (4!*4!)/(sqrt(4)*4)73 = (4! + 4! + Sqrt(,4…))/Sqrt(,4…)74 = 4!+4!+4!+sqrt(4)75 = (4!+4!/4)/.476 = 4!+4!+4!+477 = (4/.4…)^sqrt(4)-4
78 = (4!-4)·4-Sqrt(4)79 = (4/.4…)^sqrt(4)-sqrt(4)80 = ((4^sqrt(4))/,4) * sqrt(4)81 = (4-4/4)^482 = (4!-4)·4+ sqrt(4)83 = (4/.4…)^sqrt(4)+sqrt(4)84 = 44·Sqrt(4)-485=(4/.4…)^sqrt(4)+486 = 44/.4-4!87 = (4! * 4) – (4/,4…) 88 = (4^4)/4 + 4!89 = (sqrt(4)+4!)/.4+4!90 = (4 + Sqrt(4))! / (4·Sqrt(4))91 = (4! * 4) – (sqrt(4)/,4) 92 = 44 + 4! + 4!93 = 4!·4-sqrt(4/.4…)94 = (4!)*4 – 4 + Sqrt(4)95 = 4*4!-4/496 = 4 * 4! + 4 – 4 97 = 4 * 4! + 4/498 = 4! * 4 + 4 – Sqrt(4)99 = ((4! – Sqrt(4)) * Sqrt(4) ) / .4…100 = 4! * 4 + Sqrt(4) * Sqrt(4)
Como véis muchos de estos números se consiguen con contenidos matemáticos que el alumnado de primaria aún no ha estudiado, por lo que el objetivo puede ser cuántos números se han conseguido de media y distintas formas de obtener un mismo número.
Recuerda: ¡Lo importante es participar y fomentar la creatividad¡Recuerda: ¡Lo importante es participar y fomentar la creatividad¡
