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Tiling Challenge (Posted on 2024-12-04) Difficulty: 3 of 5
A square with side length 49 is completely tiled with the following non-overlapping shapes: 600 1×4 rectangles and a unit square. Find the number of possible locations of the unit square.

No Solution Yet Submitted by Danish Ahmed Khan    
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re: Parity | Comment 2 of 6 |
(In reply to Parity by Brian Smith)

Although this rules out all but the 169 identified squares, it doesn't prove all of these are actually possible.  (I do think they are possible)


Also your 'other diagonal' approach doesn't rule out a few more squares
A***A***A
*********
**B***B**
*********
A***A***A
*********
**B***B**
*********
A***A***A
But I don't think these B squares are possible.

  Posted by Jer on 2024-12-06 11:17:45
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