N is a seven digit base-14 positive integer using the digits 1 to 7 exactly once.

Determine the total number of value(s) of N that are divisible by the base-14 number 16.

So, the last 2 digits are limited to {12,32,52,72,16,36,56,76}

Within the first 5 digits:
1,4,6 add + or - 4 to the mod value (depending on position)
2,3,7 add + or - 8 to the mod value
5 adds 0 to the mod value
1 and 6 are interchangeable and 2 and 7 are interchangeable.

Examples found so far:

5146372
5641372
1457236
1452736

I suspect there are a dozen more or so maybe twice that

Edited on September 12, 2010, 2:33 pm

Posted by Larry on 2010-09-12 14:22:24