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.

Using the previous ranges (1023456789 to 9876543210: actually starting with 1023456432), and testing every multiple of 11111 in range (to be sure ten different digits) , I find 3456 cases, from 1023489765 to 9876501234 -- about a half-second computer execution time.  The only thing "analytic" about this was setting up the algorithm, about a dozen lines of code.  I would be interesting to see how a less "brute-force" method could get the exact count (as noted, the probabilities for the 796785 products in range will be slightly skewed).

Posted by ed bottemiller on 2008-10-02 17:59:41