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As depicted above, a X-pentomino is formed by using a 3x3 grid with the four of its corners removed.
Determine the maximum number of such X-pentominoes that could fit inside an 8x8 square grid without overlapping.
It is not specified that the pentominoes must conform to the grid-lines of an 8x8 square. If this is the case, the maximum number is 8:
.A....B.
AAAC.BBB
.ACCCDB.
..ECDDD.
.EEEFD..
.GEFFFH.
GGG.FHHH
.G....H.
That's the tessellation of the plane by X pentominoes, cut so one X is at each corner.
If we rotate the square by arctan(1/2) then 9 of the pentominoes in a 3x3 array can fit and the square can be reduced to a side length as small as sqrt(58).
edit: to fix the preformatting
Edited on August 27, 2023, 9:55 am
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Posted by Jer
on 2023-08-27 09:53:34 |
Two answers
