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It is possible, using a set of just 10 polyominoes, to construct any one of the 26 letters below. Can you find such a set?

enter image description here

When constructing, polyominoes may be rotated and flipped, but may not overlap.

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  • $\begingroup$ Whew, that's quite a bit more difficult than the last one! $\endgroup$ Mar 18, 2020 at 1:04
  • $\begingroup$ You enjoy challenges, right? :) $\endgroup$
    – Jens
    Mar 18, 2020 at 1:19
  • $\begingroup$ Can the tiles overlap? $\endgroup$ Mar 18, 2020 at 1:19
  • $\begingroup$ @Dmitry No. See last sentence. $\endgroup$
    – Jens
    Mar 18, 2020 at 1:20
  • $\begingroup$ Are triominoes allowed? $\endgroup$
    – Alto
    Mar 18, 2020 at 1:42

2 Answers 2

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I haven't tried one of these before; I just stumbled across the question by accident. But I think I have an answer. You can build all 26 letters if you have a set containing:

- 1 straight pentomino
- 1 straight tetromino
- 4 straight trominoes
- 2 L-shaped trominoes
- 2 dominoes

Image below:

enter image description here

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  • $\begingroup$ Thanks! Do you happen to know if there are other correct solutions? $\endgroup$
    – Dave
    Mar 18, 2020 at 10:13
  • $\begingroup$ Very nicely done! And yes there are other solutions. My own solution had 3 trominoes and 7 dominoes. $\endgroup$
    – Jens
    Mar 18, 2020 at 15:27
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Using:

9. 1 straight tetromino, 2 straight trominoes, 1 L-tromino and 5 dominoes, which is minimal in the sense that it only uses $23$ blocks, which is how many blocks both 'B' and 'R' use.

letters

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    $\begingroup$ You haven't shown that this set actually does tile all the letters though. A picture would help. $\endgroup$ Mar 18, 2020 at 10:24
  • $\begingroup$ You can almost do it with {1,3,5} -- all except K. $\endgroup$ Mar 18, 2020 at 11:38
  • $\begingroup$ Oh, but it can be done with 9 polyominoes, with an L tromino replacing domino+monomino. $\endgroup$ Mar 18, 2020 at 11:53
  • $\begingroup$ I think your E, I and S are using one extra domino than you have in your set... $\endgroup$
    – Stiv
    Mar 18, 2020 at 12:09
  • $\begingroup$ @Stiv; fixed, tnx. $\endgroup$
    – JMP
    Mar 18, 2020 at 12:16

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