Substitute each of the capital letters in bold by a different base ten digit from 0 to 9 to satisfy this set of alphametic relationships. None of the numbers can contain any leading zero.

• NATE is divisible by 3, and:
• ATEN is divisible by 7, and:
• ANTE is divisible by 11, and:
• NEAT is divisible by 17.

What are the possible value(s) that NEAT can assume?

40 minutes without computer:

9027 and 9741

Without  non-distinct digits constraint: 6936 is ok as well

Posted by Ady TZIDON on 2009-09-27 05:22:34