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I pick two whole numbers x and y between 1 and 10 inclusive (not necessarily distinct). My friend picks two numbers x - 4 and 2y + 1. If the product of my friend's numbers is one greater than the product of my numbers, then what is the product of my numbers?

 Sep 4, 2021
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This is , $(x - 4)(2y + 1) = 1 + xy.$

Solving, give $x = 9, y = 6.$ So, the product is $9 \cdot 6 = \boxed{54}$.

 Sep 5, 2021

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