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"all religions, arts and sciences are branches of the same tree. all these aspirations are directed toward ennobling man's life, lifting it from the sphere of mere physical existence and leading the individual towards freedom." albert einstein

factoid



Factoid:

111111111 * 111111111 =

12345678987654321

92 Comentarios


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Comentarios

1
De: gery Fecha: 2008-02-06 13:42

i just want to comment on that multiplication. It's not a consequence of a deep result, it's actually very simple when you do written multiplication. Additionally, you also have :
11*11 = 121
111*111 = 12321
1111*1111 = 1234321

and so on. If we were using a higher base than 10, for exemple hexadecimal, we would have :
1111111111111111*1111111111111111 =
123456789ABCDEFEDCBA987654321



2
De: Wolfger Fecha: 2008-02-06 14:35

It also equals 2345678987654321 (doing the math in hexadecimal)
and 111111110000000001 (in binary)
and nothing particularly interesting in octal...



3
De: Eduardo Padoan Fecha: 2008-02-06 15:16

In [1]: 111111111 * 111111111
Out[1]: 12345678987654321L



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De: BobCFC Fecha: 2008-02-06 17:07

Finally! A reason to use 64bit apart from the ram issue :P



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De: Duda Nogueira Fecha: 2008-02-06 17:54

try:

12345679 * 8 = 98765432

cool :)



6
De: luisbg Fecha: 2008-02-07 09:38

the hexadecimal is awesome.

and thanks duda nogueira for the reply! :)



7
De: FrnchFrgg Fecha: 2008-02-09 20:37

One other intersting number is n = 142857. When you multiply it by 2, 3, 4, 5, and 6, you get a permutation of its digits. A whole research on this number has been done by Lewis Carol...

It comes from the fact that this is the periodic decomposition of 1/7, so n*3 = 428571 is the periodic decomposition of 3/7 = 10/7 - 1, n*2 = 285714 is the periodic decomposition of 2/7 = 100/7 - 14, and so on..

The good question is "are there other such numbers" ? That is numbers such that multiplying them by the first integers you get the same digits in a different order ? If so, what is the greatest such multiplier for which it still works (necessarily < 10, since starting from 10 you're ensured to get one more digit)



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De: FrnchFrgg Fecha: 2008-02-09 20:39

Note that 142857142857 n = 1..6 is too easy an answer for the preceding riddle.



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