Enigma

El uno es misterioso

Las regularidades matemáticas no dejan de sorprender.
Lo que ahora verás tiene siglos pero aún sigue vigente dado que confirma la capacidad que matemática tiene para la generación de modelos debido a la constante presencia de regularidades propias de su comportamiento.

Lo que vamos a trabajar es histórico y por lo tanto nada novedoso, pero nos pareció interesante volver a recordarlo, para algunos, y darlo a conocer, para otros, con la simple finalidad de que las cosas útiles e inteligentes no se pierdan del conocimiento popular.

Manos a la obra:

Hagamos la siguiente multiplicación 1 x 1 = 1
Utilizaste dos unos y te resultó un número de una sola cifra.

Ahora 11 x 11 = 121
Utilizaste cuatro unos y te resultó un número de tres cifras.

Ahora 111x 111 = 12321
Utilizaste seis unos y te resultó un número de cinco cifras.

Si observas detenidamente los resultados son dos sucesiones, una creciente y otra decreciente, de uno en uno a partir de 1 y finalizando en 1. Cada resultado, entonces, es número capicúa.

Por lo tanto 11.111 x 11.111, al haber utilizado diez unos resultará un número de 9 cifras, y a su vez capicúa, entonces será: 123454321, ¿será así?

Prueba si resulta para la siguiente multiplicación:

1.111.111 x 1.111.111 =

Si todo fue bien, intenta para la siguiente multiplicación:

111.111.111 x 111.111.111 =

Si no te resulta ¡por favor nos avisas!

0
Su voto: Nada

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Sporting a tonal black primeknit upper to further emphasize its midsole, the sneaker also features a leather caging system for additional flair, while the recognizable TPU heel counter is blacked-out Adidas NMD as well.adidas Originals recently debuted an all-new adidas Ultra Boost Uncaged Khaki colorway as part of their Spring 2017 lineup.This adidas Ultra Boost features a combination of Khaki and Brown throughout its Primeknit upper accented Eqt Adidas with a ribbed sock-like collar. Other details include tonal flat laces, a TPU heel unit, full-length White Boost midsole atop a rubber outsole.Already sold-out at Kith, you may want to check your local adidas Originals locations Yeezy Boost 350 Oxford Tan for availability of this adidas Ultra Boost Uncaged “Khaki” colorway.adidas Originals and Titolo are connecting for another collaboration for 2017. 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Interesante el tema !En base

Interesante el tema !
En base 8 (subíndice "o")
1o x 1o = 1o
11o x 11o = 121o
111o x 111o = 12321o
....
....
111111o x 111111o = 12345654321o
1111111o x 1111111o = 1234567654321o
11111111o x 11111111o = 123457007654321o - se termina la regularidad !

Si miramos las series obtenidas en base 10 y base 8 , parecería indicarnos que la regularidad se rompe cuando realizamos el producto de N = Base veces el uno, al introducir la base 2 se ve que NO es así ya que parece repetirse ad infinitum.-
Comienzo a probar con la base 16, aunque tengo problemas para chequear el resultado del producto más allá de la siguiente operación: 11.111.111h x 11.111.111.111h
1h x 1h = 1h
11h x 11h = 121h
....
....
11111111h x 11111111h = 123456787654321h

¿¿¿¡¡¡ ESTOS RESULTADOS NO SON CONFIABLES !!!???
PARECE QUE FALLA EL ALGORITMO DE CAMBIO DE BASE DE MI CALCULADORA

111.111.111h x 111.111.111h = 2345678987654321h
1.111.111.111h x 1.111.111.111h = 456789A987654321h
11.111.111.111h x 11.111.111.111h = 6789ABA987654321h
111.111.111.111h x 111.111.111.111h = 89ABCBA987654321h
1.111.111.111.111h x 1.111.111.111.111h = ABCDCBA987654321h

Imagen de Oscar Isnardi

esto es macanudo. Ciertoel

esto es macanudo. Ciertoel momento en que se rompe la regularidad, ahora bien, ¿Qué pasa con base 2? ¿no nos pasa lo mismo y luego cambia la regla?, estoy pensando al escribir de la máquina, aún no hice demostración alguna, a eso voy.

Imagen de geeme

Le paso unos cálculos : Tomo

Le paso unos cálculos :
Tomo la base 8: el subíndice "o" indica base 8
1o x 1o = 1o
11o x 11o = 121o
111ox111o= 12321o
1111o x 1111o = 1234321o
11111o x 11111o = 123454321o
111111o x 111111o = 12345654321o
1111111o x 1111111o = 1234567654321o
11111111o x 11111111o = 123457007654321o - se rompió la regularidad ?!

Observe lo siguiente: utilizo la base 2 - binaria - utilizo el subíndice "b" en la notación:
1b x 1b = 1b
11b x 11b = 1001b
111b x 111b = 110001b
....
....
11111111111b x 11111111111b = 1111111111000000000001b

En la base 2 (binaria) parece "existir" una regla que no se "termina" ?!?!
n unos en la base binaria multiplicados por n unos en la base binaria dá un número que resulta ser (n-1) veces el número uno seguido de n 0 (ceros) y un último número 1 !?!?!?

A ver si alguno más prueba !!!

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muy bueno lo tuyo. Así se

muy bueno lo tuyo. Así se hace matemática. Ahora te propongo que mires en base 8 y verás que SI se rompiuó la regularidad en que falta un 6, suponiendo que tus resultados sean correctos, que por supuesto, no revisé porque no es mi función corregir operaciones.

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se rompió la regularidad,

se rompió la regularidad, pero ahora nos taca preguntarnos ¿por qué será?vamos a estudiar. ¿si cambiamos de base numércia y en lugar de base decimal tomamos base 9, ¿no resultará la regularidad original?

Imagen de geeme

A ver si entiendo su

A ver si entiendo su propuesta: Ud. propone cambiar la base del número 1.111.111.111 a la base 9, realizar el producto y ver que resultado se obtiene en la base 9 ? Si cambio la base del 1.111.111.111 a la base 16 ? (me resulta más rápido) - Aguardo su comentario.

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si puede ser mas rápido, pero

si puede ser mas rápido, pero la pregunta es ver si resulta la regularidad, y si así fuese ver porqué resulta. digamos que cualquier base es lo mismo para el análisis, no importa la rapidez con la que opere.

Imagen de geeme

A ver si entiendo su

A ver si entiendo su propuesta: Ud. propone cambiar la base del número 1.111.111.111 a la base 9, realizar el producto y ver que resultado se obtiene en la base 9 ? Si cambio la base del 1.111.111.111 a la base 16 ? (me resulta más rápido) - Aguardo su comentario.

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El uno es misterioso

La regularidad se cumple : 111.111.111 x 111.111.111 (resultado : 12345678987654321) , al agregar un dígito más, o sea
1.111.111.111 x 1.111.111.111 no se observa la regularidad

Imagen de Oscar Isnardi

alguna respuesta traté da

alguna respuesta traté da darte, fijate si te satisface, seguimos en contacto

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