I usually spend max 20 minutes playing with something like that, then hours or even days finding a good SAT encoding for the puzzle so I can easily solve it with a program. (I can recommend this strategy to anyone who wants to improve their SAT or SMT skills.)
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This is the first one I solved like that after *days* of trying it by hand. (The puzzle was passed to me through a series of people who all tried and failed.) This are five 1x1x1 pieces, five 2x2x3 pieces, six 1x2x4 pieces and a 5x5x5 box. 1/2pic.twitter.com/MxKjfMCozZ
And here is the program that solves it: https://github.com/YosysHQ/yosys/blob/master/libs/ezsat/puzzle3d.cc … Not counting mirror images and rotations there are 4 unique solutions. (The program generates OpenSCAD models: https://github.com/YosysHQ/yosys/blob/master/libs/ezsat/puzzle3d.scad … You can slice and rotate in OpenSCAD to inspect the 3D model. 2/2pic.twitter.com/lpkGhOeOBZ
