One type of self referential number is one in which each digit represents the number of occurrences of that digit in the number itself. For exmaple 21200 has 2 zeros, 1 one, 2 twos, 0 threes, and 0 fours.

The atbash substitution cipher has the reversed alphabet as the encoding rule: A means Z, B means Y, C means X, etc. For decimal digits, the atbash equivalent is simply 9 minus the digit.

Find a 10 digit atbash self referential number such that the leftmost digit is 9 minus the number of zeros, the next digit is 9 minus the number of ones, etc.

The answer is 9998999873.  This was found by noting that it is 9999999999 - the reverse of a normal 10-digit self-referential number, which is 6210001000.  

Posted by tomarken on 2024-02-27 08:26:40