MathDB

Determine all ten-digit numbers whose decimal

\overline{a_0a_1a_2a_3a_4a_5a_6a_7a_8a_9}

is given by such that for each integer

j

with

0\le j \le 9, a_j

is equal to the number of digits equal to

j

in this representation. That is: the first digit is equal to the amount of "

0

" in the writing of that number, the second digit is equal to the amount of "

1

" in the writing of that number, the third digit is equal to the amount of "

2

" in the writing of that number, ... , the tenth digit is equal to the number of "

9

" in the writing of that number.

Problem Statement