This week’s problem is offered more in the spirit of a light and pleasant diversion — I don’t think you’ll need any deep insight to solve it. (A little persistence may come in handy though!)

Define a triomino to be a figure congruent to the union of three of the four unit squares in a 2 \times 2 square. For which pairs of positive integers (m, n) is an m \times n rectangle tileable by triominoes?

Please submit solutions to topological[dot]musings[At]gmail[dot]com by Wednesday, July 3, 11:59 pm (UTC); do not submit solutions in Comments. Everyone with a correct solution will be inducted into our Hall of Fame! We look forward to your response. Enjoy!

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