(I don't think I've seen this before, but having figured it out and written it down I have a bit of a sense of déjà vu...)
A bit of notation:
In other words,
Here's a fairly crappy diagram that may help follow the above:
By the look of it, this puzzle comprises one of each of the 12 different pentomino shapes. In which case, an example packing can be found on the Wikipedia page for 'Pentomino', as follows:
If you would like a little history, the 6x10 case was first solved as far back as 1960 by Colin Brian Haselgrove and Jenifer Haselgrove, and there are apparently 2,339 ...
This puzzle of mine appears to have languished with no solution for some time. I don’t remember the solution I initially had in mind, but I thought of one recently that might be of interest, so answering my own puzzle here.
It suffices to show that for any $n$, there exists an $n$-gon inscribed in the unit circle with pairwise-distinct rational distances, ...
I wrote a solver for this (and related polycubes) using or-tools.
You can see it here https://github.com/MrBenGriffin/or-tools-fun
There are many related puzzles!
A standard pentomino puzzle is to tile a rectangular box with the pentominoes, i.e. cover it without overlap and without gaps. Each of the 12 pentominoes has an area of 5 unit squares, so the box ...