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 15 Triominoes (Posted on 2016-07-26)
A tiling is said to be fault free if there are no straight lines which can split the tiling without intersecting a tile.

Two L-triominoes trivially form a fault free tiling of a 2x3 rectangle.

Find a fault-free tiling of a 9x5 rectangle using 15 L-triominoes.

 No Solution Yet Submitted by Brian Smith No Rating

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 re(2): Harder case Comment 4 of 4 |
(In reply to re: Harder case by Brian Smith)

A fault splits the rectangle into two smaller rectangles.  There are only three possibilities to consider because the areas have to be multiples of 3:

1x9 and 4x9 (immediately rule out)
2x9 and 3x9
3x5 and 6x5

In the remaining cases there is a strip 3 spaces wide.
Try to tile the edge of this strip, the only possibility for the first row of squares as that one triomino covers two and another covers one.  This is a 2x3 rectangle.
So the 3x5 or 3x9 must be covered by 2x3 rectangles.  Since 5 and 9 are both odd, both are impossible.

 Posted by Jer on 2016-07-27 21:31:41

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