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I enjoyed this puzzle. Each step follows naturally from the last until the rectangle is filled. Reasoning Putting a large L in a corner leads to a sequence of placements that unavoidably fi...
#1: Initial revision
by
trichoplax
·
2026-09-11T23:46:24Z (5 days ago)
I enjoyed this puzzle. Each step follows naturally from the last until the rectangle is filled. <details> <summary>Reasoning</summary> <!-- An empty line is required for markdown to render --> - Putting a large L in a corner leads to a sequence of placements that unavoidably fill a 4 by 6 rectangle, leaving a 5 by 6 rectangle to be filled. This requires 30 squares, which can only be 6 small Ls, which do not fit. Each corner therefore has a small L. Their corners must be in the corners of the rectangle otherwise progress quickly becomes impossible. - This leaves spaces of height 4 on the left and right which must be filled by large L's otherwise all subsequent placements leave gaps. One of the large L's must be rotated 180 degrees relative to the other otherwise they will overlap. - The resulting spaces at the top and bottom cannot accommodate a large L, and can only accommodate a small L in one orientation. - This leaves 2 spaces the exact size and shape of a small L. <details> <summary>Solution</summary> <!-- An empty line is required for markdown to render --> [![2 L shapes from 7 squares each and 8 L shapes from 5 squares each arranged in a 9 by 6 rectangle][solution]][solution] <details> <summary>Animation</summary> <!-- An empty line is required for markdown to render --> [![L shapes appearing one at a time in the order described][animation]][animation] </details> </details> </details> I believe this is the only possible solution (apart from its mirror reflection). [solution]: https://raw.githubusercontent.com/trichoplax/l-shapes-6-by-9-rectangle-puzzle-solution/refs/heads/main/solution.svg [animation]: https://raw.githubusercontent.com/trichoplax/l-shapes-6-by-9-rectangle-puzzle-solution/refs/heads/main/animation.svg