Find the biggest integer N such that:
1. All its digits are distinct.
2. Each of these digits divides N.

Only a p&p solution requested.

Bonus: What would be the answer, if one of N"s digits were exempted from being its divider?

(In reply to manual solution to bonus is wrong by Charlie)

Yes. This was the subject of a problem in New Scientist, April 2011.

The key to the solution is divisibility by 7 but there are a tedious number of alternatives to be eliminated.

I did not win the prize, unfortunately.

Edited on October 14, 2014, 9:07 am

Posted by broll on 2014-10-14 09:02:39