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LAS TORRES DE HANOI CONOZCA Y RESUELVA ESTE JUEGO MATEMATICO JOSE GUILLERMO RODRIGUEZ ALARCON
LAS TORRES DE HANOI Las torres de Hanoi son un juego-problema matemático Tiene tres postes, y en uno de ellos hay una pirá...
Para entender mejor este juego-problema matemático, comencemos por pasos, trabajemos solo con un disco, para pasarlo a otr...
Ahora realicemos el ejercicio con dos discos, y observemos cuantos  movimientos son  necesarios, para colocarlos ordenadam...
3 Fueron necesarios tres movimientos Recuerda que la idea es hacer el menor número de movimientos para lograr el objetivo ...
1 2
3 4 5 6
7 Con cuatro discos la formula quedaría  2 4-1  = 15 o sea, que quince es  el menor número de movimientos posibles para mo...
1 2 3 4
5 6 7 8
9 10 11 12
13 14 15
Si observamos detenidamente cada que sumamos un disco  los primeros movimientos se repiten y se van sumando los restantes ...
<ul><li>2  Un disco </li></ul><ul><li>_____ </li></ul><ul><li>3  Dos discos </li></ul><ul><li>3 </li></ul><ul><li>_____ </...
<ul><li>Recuerda, sin importar el número de discos que vayas  a utilizar,  </li></ul><ul><li>siempre debes empezar desde e...
Ahora inténtalo con más discos, tu puedes , solo debes concentrarte  y lo lograras, te dejo las formulas con el mínimo núm...
 
 
 
 
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Manual Torres De Hanoi

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Manual Torres De Hanoi
jose guillermo rodriguez alarcon

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Manual Torres De Hanoi

  1. 1. LAS TORRES DE HANOI CONOZCA Y RESUELVA ESTE JUEGO MATEMATICO JOSE GUILLERMO RODRIGUEZ ALARCON
  2. 2. LAS TORRES DE HANOI Las torres de Hanoi son un juego-problema matemático Tiene tres postes, y en uno de ellos hay una pirámide de discos de distinto tamaño. El objetivo es mover todos los discos de un poste a otro, pero solo puedes mover un disco a la vez, además de que no puedes poner un disco grande encima de uno pequeño
  3. 3. Para entender mejor este juego-problema matemático, comencemos por pasos, trabajemos solo con un disco, para pasarlo a otro poste solo será necesario un movimiento
  4. 4. Ahora realicemos el ejercicio con dos discos, y observemos cuantos movimientos son necesarios, para colocarlos ordenadamente en otro poste 1 2
  5. 5. 3 Fueron necesarios tres movimientos Recuerda que la idea es hacer el menor número de movimientos para lograr el objetivo Los especialistas dicen que para resolver este ejercicio se debe utilizar La formula 2 n-1 (dos a la ene menos uno) donde 2 hace referencia a la numeración binaria como representante absoluto y ene es el número de discos a utilizar , o sea que: 2 1-1 = 1 , 2 2-1 = 3 , 2 3-1 = 7 De donde deduzco que si tengo tres discos, serán necesarios siete movimientos para moverlos ordenadamente a otro poste, veamos :
  6. 6. 1 2
  7. 7. 3 4 5 6
  8. 8. 7 Con cuatro discos la formula quedaría 2 4-1 = 15 o sea, que quince es el menor número de movimientos posibles para mover ordenadamente los discos a otro poste, veamos :
  9. 9. 1 2 3 4
  10. 10. 5 6 7 8
  11. 11. 9 10 11 12
  12. 12. 13 14 15
  13. 13. Si observamos detenidamente cada que sumamos un disco los primeros movimientos se repiten y se van sumando los restantes hasta completar el resultado de la formula. También observamos que si numeramos los discos de arriba hacia abajo, los discos impares giran en un sentido y los pares en el sentido contrario, en el caso de los ejercicios anteriores los discos 1 y 3 giran hacia la derecha (de la pantalla) y los discos 2 y4 giran hacia la Izquierda Teniendo en cuenta las observaciones anteriores, podemos establecer un algoritmo recursivo que nos permite solucionar el juego- problema con diferentes números de discos Tomaremos la torre del centro como la torre numero uno, la torre de la derecha como La torre numero dos, y la torre de la izquierda como la numero tres Al lado de los movimientos colocaremos el numero de discos, una línea separa los movimientos según el numero de discos, veamos :
  14. 14. <ul><li>2 Un disco </li></ul><ul><li>_____ </li></ul><ul><li>3 Dos discos </li></ul><ul><li>3 </li></ul><ul><li>_____ </li></ul><ul><li>2 Tres discos </li></ul><ul><li>1 </li></ul><ul><li>3 2 </li></ul><ul><li>2 </li></ul><ul><li>_____ </li></ul><ul><li>3 Cuatro discos </li></ul><ul><li>3 </li></ul><ul><li>2 1 </li></ul><ul><li>1 </li></ul><ul><li>3 </li></ul><ul><li>2 </li></ul><ul><li>1 3 </li></ul><ul><li>2 3 </li></ul><ul><li>2 Cinco discos </li></ul><ul><li>1 </li></ul><ul><li>3 2 </li></ul><ul><li>2 </li></ul><ul><li>1 </li></ul><ul><li>3 </li></ul><ul><li>2 1 </li></ul><ul><li>1 </li></ul><ul><li>3 2 </li></ul><ul><li>2 </li></ul><ul><li>1 3 </li></ul><ul><li>3 </li></ul><ul><li>2 </li></ul><ul><li>1 </li></ul><ul><li>3 2 </li></ul><ul><li>2 </li></ul><ul><li>_____ </li></ul><ul><li>1 3 Seis discos </li></ul><ul><li>3 </li></ul><ul><li>2 1 </li></ul><ul><li>1 </li></ul><ul><li>3 </li></ul><ul><li>2 </li></ul><ul><li>1 3 </li></ul><ul><li>3 </li></ul><ul><li>2 1 </li></ul><ul><li>1 </li></ul><ul><li>3 2 </li></ul><ul><li>2 </li></ul><ul><li>1 </li></ul><ul><li>3 </li></ul><ul><li>2 1 </li></ul><ul><li>1 </li></ul><ul><li>3 </li></ul><ul><li>2 </li></ul><ul><li>1 3 </li></ul><ul><li>3 </li></ul><ul><li>2 </li></ul><ul><li>1 </li></ul><ul><li>3 2 </li></ul><ul><li>2 </li></ul><ul><li>1 3 </li></ul><ul><li>3 </li></ul><ul><li>2 1 </li></ul><ul><li>1 </li></ul><ul><li>3 </li></ul><ul><li>2 </li></ul><ul><li>1 3 </li></ul><ul><li>2 3 </li></ul>
  15. 15. <ul><li>Recuerda, sin importar el número de discos que vayas a utilizar, </li></ul><ul><li>siempre debes empezar desde el principio (un disco) </li></ul><ul><li>El juego tiene una relación estrecha con la manera como se representa </li></ul><ul><li>en el sistema binario, por lo tanto si investigas sobre el tema, </li></ul><ul><li>entenderás mejor </li></ul><ul><li>El trabajar las torres de Hanoi le permitirá a los niños relacionarse con </li></ul><ul><li>temas como : </li></ul><ul><li>Sistemas numéricos </li></ul><ul><li>Sistema binario </li></ul><ul><li>Potenciación </li></ul><ul><li>Matemática de posición </li></ul><ul><li>Algoritmos recursivos </li></ul><ul><li>Pensamiento conjetural </li></ul><ul><li>Resolución de problemas </li></ul><ul><li>Comunicación matemática </li></ul><ul><li>Lógica </li></ul><ul><li>Motricidad </li></ul>
  16. 16. Ahora inténtalo con más discos, tu puedes , solo debes concentrarte y lo lograras, te dejo las formulas con el mínimo número de movimientos, para realizarlo con siete, ocho, nueve y diez discos 2 7-1 = 127 Movimientos 2 8-1 = 255 Movimientos 2 9-1 = 511 Movimientos 2 10-1 = 1023 Movimientos Si lo quieres intentar con más discos , ya lo puedes calcular, hecha mano de la formula, el patrón y el algoritmo y listo !

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