Find four distinct positive integers such that:

(i) The sum of all the four positive integers is 31, and:
(ii) Precisely one of four numbers is odd, and:
(iii) The only odd number is the largest and it is not prime, and:
(iv) The absolute difference between the middle two numbers is 2.

There are not many cases to try

2 4 6 19 <-- fail, prime

2 6 8 15 <-- SOLUTION

2 10 12 11 <-- odd number not largest, so no more possibilities starting with 2

4 6 8 13 <-- fail, prime

4 8 10 9 <-- odd number not largest, so no more possibilities starting with 4

6 8 10 7 <-- odd number not largest, so no more possibilities starting with 6 or higher

Posted by Steve Herman on 2015-03-18 08:49:44