I've probably seen this done somewhere else but I can't think where or else I'd drop a link in and let them explain it better than I can. Basically, the idea is to create a rectangle (or another shape, I won't judge) out of the pentominoes and hexominoes together - 270 units total so you've got a few choices here. But, there are a few restrictions you can place on the positioning of the pentominoes.
For the easiest option, forbid the pentominoes from touching each other (either by sharing an edge or touching point-to-point.) Or if you want to ramp up the challenge a bit, prohibit the pentominoes from touching the edge of the rectangle too. This is essentially a hexomino construction with 12 pentomino-shaped holes in it, if you want to think about it that way. Below are pictures for the 15x18 and 10x27 cases, but there are several other aspect ratios possible, the thinner the rectangles become the harder I imagine it'll be to keep the pentominoes away from one another.
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| Fig. 1: The 15x18 solution in a colour scheme that would have Ikea's lawyers frothing at the mouth |
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| Fig. 2: A 10x27 solution |
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