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The Sisyphus String: 123

Community Veteran
Posts: 1,571
Thanks: 3
Registered: 13-04-2007

The Sisyphus String: 123

Work this out then
Suppose we start with any natural number, regarded as a string, such as 9,288,759. Count the number of even digits, the number of odd digits, and the total number of digits. These are 3 (three evens), 4 (four odds), and 7 (seven is the total number of digits), respectively. So, use these digits to form the next string or number, 347.
Now repeat with 347, counting evens, odds, total number, to get 1, 2, 3, so write down 123. If we repeat with 123, we get 123 again. The number 123 with respect to this process and the universe of numbers is a mathemagical black hole. All numbers in this universe are drawn to 123 by this process, never to escape.
But will every number really be sent to 123? Try a really big number now, say 122333444455555666666777777788888888999999999(or pick one of your own).
The numbers of evens, odds, and totalare 20, 25, and 45, respectively. So, our next iterate is 202,545, the number obtained from 20, 25, 45. Iterating for 202,545 we find 4, 2, and 6 for evens, odds, total, so we have 426 now. One more iteration using 426 produces 303, and a final iteration from 303 produces 123.
At this point, any further iteration is futile in trying to get away from the black hole of 123, since 123 yields 123 again.
1 REPLY
Lurker
Grafter
Posts: 1,867
Registered: 23-10-2008

Re: The Sisyphus String: 123

Interestingly, you could argue (as many have) that 0 is not an even number.
So if you try the same assuming its an odd number, you get the same net result. (Try it!)
But then the argumentative might remind us that 0 is not an odd number either; so try the above exercise whilst counting zero as neither odd nor even. (Count it as a digit though)
Or, if its not odd, or even, perhaps we should discount it altogether. (Guess what - same result)
Good eh?