by Howard Williams

Published Sunday July 12 2026 (link)

I have ten cards on which are written 20 different positive integers, with one integer on each side of the cards. The total of the integers on the front of the ten cards equals the total of the integers on the back. The total of the integers on each card is also the same.

The numbers on the front of the first nine cards are 2, 15, 17, 21, 24, 31, 35, 36 and 44. If I told you how many prime numbers are on the cards you should be able to tell me the two numbers on the tenth card.

In ascending order, what are the numbers on card ten?