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Things I have learned. Things I built, broke, and eventually figured out.
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82a30101bb26b8fee0b96bac5a57a8b0
How to solve the 2D rectangle variant of the IQ fit puzzle: math and code
Jul 26, 2026 · 17 min
Twelve ball-pieces, an 11×5 board of fifty-five holes, and one exact covering. Symmetry cuts the search space for free via the dihedral group, a counting argument proves that a full board is a solved board, and a Rust solver packs the whole grid into a single u64 so every placement is a bitwise AND.
algorithm
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group-theory
·
math
asymmetric (F)
stab = 1 → 8
mirror symmetry (U)
stab = 2 → 4
reflect = same look
|orbit| = 8 / |stab|