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
square. For which pairs of positive integers
is an
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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July 3, 2008 at 4:52 am
Solution to POW-6: Tiling with Triominoes « Todd and Vishal’s blog
[...] Problem Solving, Problem of the Week (POW) by Todd Trimble Dang! No solutions were received for last week’s problem; a couple of people made a decent start but didn’t send in a complete solution before time [...]
April 21, 2013 at 2:50 am
Tristan
An $m\times n$ rectangle is tileable by triominoes if and only if $m>1$ and $n>1$ (obviously), and $6\mid mn$.