The (almost really) Complete Works of Lewis Carroll

A Mysterious Number

Source: Chatterbox, February 1897 (authorship not certain, but a very similar manuscript exists)

The number 142,857 does not at first sight appear to have anything odd about it, yet there are some strange things about it.

Let us multiply it by the numbers 2 to 7 and see the result.

142,857 by 2 is 285,714.
142,857 by 3 is 428,571.
142,857 by 4 is 571,428.
142,857 by 5 is 714,285.
142,857 by 6 is 857,142.
142,857 by 7 is 999,999.

The first five products, you will observe, are composed not only of the same figures, but of the same figures in the same order, though beginning with a different figure each time. And the strangest part of it all is that 142,857 multiplied by 7 is 999,999, but after that point the products lose their oddity.