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Glob Tiling (Posted on 2025-03-01) Difficulty: 3 of 5
A glob is a polygon like a Tetris piece, but made out of 7 squares instead of four, attached edge-to-edge to form a single polygon. It is known that there are exactly 108 different globs. Is it possible to tile a 28 × 27 rectangle using each glob exactly once?

No Solution Yet Submitted by Danish Ahmed Khan    
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Solution Solution | Comment 1 of 4
It is not possible.

Since 28*27=108*7, the rectangle must be completely tiled with no voids. However, least one of the tiles will contain a void e.g.

XXX
X  X
XX

which cannot be filled by any other tile.

Edited on March 1, 2025, 11:07 am
  Posted by broll on 2025-03-01 11:07:12

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