Problem of the Month (April 16th, 2026)

During this session, we had students attempt to solve the problem of the month for April. The question at hand was the problem of the month by the Mathematical Association of America: [PDF Download]

Given a deck of 32 cards with 10 red cards numbered 1 to 10 (i.e. there is a red card with a number 1 on it, a red card with a number 2 on it, and so on), 10 blue cards numbered 1 to 10, and 10 yellow cards numbered 1 to 10, and 2 white cards, both numbered 0. A card with the number \( m \) is worth \( 2m \) points.

(a) We say a group of cards is good if the sum of their points is 2026, and we say a group of cards is bad if the sum is 2025. Calculate the number of “good groups” and the number of “bad groups”.

(b) Modify the deck of cards to use 42 cards by adding 10 purple cards numbered 1 to 10 with the same rule. Calculate the number of “good groups” and the number of “bad groups”.

Computer or AI assisted/generated solutions will not be accepted.