# 2021-2022 Math Prize Problem #5

Each month the Mathematics Department offers a math prize problem – a mathematical brain teaser. These problems do not require advanced knowledge of mathematics, just a curious mind and a willingness to slug it out with the problem.

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*Partition the set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11} into two sets, A and B, so that the product, (sum of values in A) × (sum of values in B), is as large as possible. For example, if A = {1, 4, 5, 11} and B = {2, 3, 6, 7, 8, 9, 10}, then the product is 21 × 45 = 945.*

*The first correct submission wins a first prize of 25 dining dollars. All other correct submissions receive recognition and bragging rights, and one of these submissions is randomly selected for a second prize of 15 dining dollars. All are welcome to participate, but prizes are for MMC students only.*

#### Happy Solving!

**Published:** May 11, 2022