Find the two highest numbers consisting each of 6 DISTINCT digits such that each when divided by any of the numbers 7, 17, 66 leaves a remainder of 5?
Since 7, 17 and 66 are relative primes we can just look at their product: 7854.
So we want numbers congruent to 5 mod 7854.
What I did was find the largest 6 digit number: 997463 and work my way down by 7854's scanning the list. It doesn't take long to arrive at:
903215 and 895361.

Posted by Jer
on 20130906 10:45:10 