Um Cálculo Curioso
Autor: MATEMÁTICA DA INFORMAÇÃO | Publicado: 2014-12-05T02:15:00-08:00

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Um Cálculo Curioso

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; Para
você se divertir com seus amigos, execute os passos a seguir e veja o
resultado:

Passo 1 – Escreva um número de três algarismos, por exemplo
217;

Passo 2 – Repita-o obtendo 217.217

Passo 3 – Divida este número por 7, o resultado por 11 e o
último por 13. Para o caso temos: 

217.217 : 7 = 31.031

31.031 : 11 = 2.821

2.821 : 13 = 217

Que é o número pensado inicialmente. Este procedimento
funciona para qualquer número de 3 algarismos.

A Explicação: 

i.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
7 x 11 x 13 = 1001

ii.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
abc x 1.001 = abc (1.000 + 1) = abc x 1000 + abc
x 1 &nbsp;= abc.000 + abc = abc.abc



Fonte: Ian Stewart; Almanaque das Curiosidades Matemáticas.