Just rearrange the 13 checkered polyominoes shown below to form a chessboard. The solution is unique and unusual.

Clarification: The pieces may be reflected; the coloring on the back is as if the ink went through the paper.

The fact that only four pentomino colorings lead to unique solutions makes this surprise a little rarer too.

(Note: I think this puzzle is original, but please feel free to delete this if I'm mistaken)

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    $\begingroup$ A similar puzzle can be found in the October 1961 issue of the Eureka journal in the article titled, “EDSAC to the Rescue”. This journal was published by The Cambridge University Mathematical Society. $\endgroup$ Feb 4 at 6:22
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    $\begingroup$ I assume rotations are allowed, but can the polyominos be flipped/reflected? $\endgroup$
    – fljx
    Feb 4 at 10:36
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    $\begingroup$ @WillOctagonGibson That version uses 12 pieces including a heptomino. A better ancestor of this puzzle was given by H.E.Dudeney in his 1907 book "The Canterbury Puzzles and Other Curious Problems". His Broken Chessboard Puzzle also uses the 12 pentominos and square tetromino, but they have a different colouring than the puzzle given here and may not be turned over. $\endgroup$ Feb 4 at 12:11
  • $\begingroup$ What do you mean by 'the coloring on the back' and the reference to 'the paper'? Did you find this puzzle somewhere else originally? Was there another image provided that explains this first remark? Thanks. $\endgroup$
    – Stiv
    Feb 6 at 7:49
  • $\begingroup$ @Stiv Since the pieces can be turned over, the colors on the other side must be specified; I was trying to explain that they are not inverted. As for the source, I ran a computer analysis of all uncolored packings of the 8x8 square with pentominoes and the square tetromino to find the colorings with unique solutions. $\endgroup$ Feb 6 at 9:34

1 Answer 1


I was curious what could possibly be so unusual in the solution.

I adapted a program I had for solving pentominos and came up with.

enter image description here

And ... I still don't see what is unusual about it.

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    $\begingroup$ IMO the most unusual thing about the solution is that the I-pentomino is fully internal, not touching the border at all. $\endgroup$ Feb 6 at 20:37
  • $\begingroup$ Ah yes, that makes sense, thank you. $\endgroup$
    – Florian F
    Feb 6 at 22:14
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    $\begingroup$ OK, I checked, the standard 10x6 pentomino puzzle has only 11 solution with piece I completely internal. I was wondering whether there were any at all. $\endgroup$
    – Florian F
    Feb 7 at 21:45

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