# Polyominoes to construct alphabet

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?

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

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

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:

• Thanks! Do you happen to know if there are other correct solutions?
– Dave
Mar 18 '20 at 10:13
• Very nicely done! And yes there are other solutions. My own solution had 3 trominoes and 7 dominoes.
– Jens
Mar 18 '20 at 15:27

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.

• You haven't shown that this set actually does tile all the letters though. A picture would help. Mar 18 '20 at 10:24
• You can almost do it with {1,3,5} -- all except K. Mar 18 '20 at 11:38
• Oh, but it can be done with 9 polyominoes, with an L tromino replacing domino+monomino. Mar 18 '20 at 11:53
• I think your E, I and S are using one extra domino than you have in your set...
– Stiv
Mar 18 '20 at 12:09
• @Stiv; fixed, tnx.
– JMP
Mar 18 '20 at 12:16