How many positive 10-digit integers of the form ABCDEFGHIJ, with non leading zeroes and each letter representing a different base 10 digit from 0 to 9, are divisible by 11,111 ?

Note : Try to solve this problem analytically, although computer program/ spreadsheet solutions are welcome.

i solved it with a perl script.
perl -le'$x=11_111; for(my $i=1;$i*$x < 9876543210; $i++) { print $x*$i }' | perl -ne'print if /0/&&/1/&&/2/&&/3/&&/4/&&/5/&&/6/&&/7/&&/8/&&/9/' | perl -pe'$i++}{$_=$i'

in the first section i form the list of all the multiples of 11,111, and in the second part, i eliminate the non-pandigital numbers, and in the third, i count them.

Posted by Pete on 2008-10-02 13:25:08