For most integer
s, if you reverse the digit
s and add it to itself, it quickly becomes a palindromic number
, that is, the digits are the same forwards and backward. For example, start with 79:
79 + 97 = 176
176 + 671 = 847
847 + 748 = 1585
1585 + 5851 = 7546
7546 + 6457 = 14003
14003 + 30041 = 44044
Until you get to 196, all the integers become palindromes quickly.
Except for the number 196. In 1990, John Walker
tested it by adding itself until it had become a number with 1,000,000 digits, and it still wasn't palindromic. In 1995 someone tested out to 2,000,000 with no success.
It seems strange that 196 should be such a special number. Of course, this is all in the totally arbitrary base 10. According to mathworld, the Palindromic Number Conjecture has been proven false in base 2, since the number 10110 never produces a palindrome.
These numbers can be viewed as Clues from the keeper of the vat.