Question

A number is called ‘interesting’ if it is divisible by 11,111. How many 10-digit interesting numbers are there?

Answer 1

If all digits are different, they must be all ten digits. In particular, the digit sum is 45
45 and hence our number is a multiple of 9
9. Thus we are in fact looking for certain multiples of 99999. This reduces your
range down to about 90000 possibilities - still unfeasible do work out by hand.

answer is 3456