Determine all possible values of a 5-digit positive integer N, such that:

1. The first two digits of N, read as a two digit number, are three times the third digit, and:
2. The last two digits of N (read as a two digit number) are twice the third digit, and:
3. The sum of all the digits of N is 27.

Prove that there are no others.

(In reply to Proof by Charlie)

The middle digit must be a multiple of 3 for the sum of digits to be a multiple of 9.

You only need to check 3, 6 and 9

Posted by Jer on 2014-04-24 01:32:35