A nine digit number has the property where the first digit equals the number of zeros and ones used in the number, the second digit equals the number of ones and twos used in the number, the third digit equals the number of twos and threes used in the number, etc. through the ninth digit equals the number of eights and nines used in the number. What could the number be?

A ten digit number has a similar property to the nine digit number. The first digit equals the number of zeros and ones used in the number, the second digit equals the number of ones and twos used in the number, etc. through the ninth digit. And also, the tenth digit equals the number of zeros and nines used in the number. What could this number be?

(In reply to Solution & method by Avin)

Yes, after only 5 iterations you get a repeat on part 2:

8  0  0  0  0  0  0  0  0  8
8  0  0  0  0  0  0  2  2  8
6  2  2  0  0  0  0  2  2  6
4  4  4  0  0  2  2  0  0  4
4  2  2  4  4  0  0  0  0  4
4  2  2  4  4  0  0  0  0  4

Posted by Charlie on 2005-09-23 20:00:41