15
$\begingroup$

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.

$\endgroup$
  • $\begingroup$ Whew, that's quite a bit more difficult than the last one! $\endgroup$ – Rand al'Thor Mar 18 at 1:04
  • $\begingroup$ You enjoy challenges, right? :) $\endgroup$ – Jens Mar 18 at 1:19
  • $\begingroup$ Can the tiles overlap? $\endgroup$ – Dmitry Kamenetsky Mar 18 at 1:19
  • $\begingroup$ @Dmitry No. See last sentence. $\endgroup$ – Jens Mar 18 at 1:20
  • $\begingroup$ Are triominoes allowed? $\endgroup$ – Alto Mar 18 at 1:42
16
$\begingroup$

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

| improve this answer | |
$\endgroup$
  • $\begingroup$ Thanks! Do you happen to know if there are other correct solutions? $\endgroup$ – Dave Mar 18 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 at 15:27
15
$\begingroup$

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

| improve this answer | |
$\endgroup$
  • 1
    $\begingroup$ You haven't shown that this set actually does tile all the letters though. A picture would help. $\endgroup$ – Rand al'Thor Mar 18 at 10:24
  • $\begingroup$ You can almost do it with {1,3,5} -- all except K. $\endgroup$ – Daniel Mathias Mar 18 at 11:38
  • $\begingroup$ Oh, but it can be done with 9 polyominoes, with an L tromino replacing domino+monomino. $\endgroup$ – Daniel Mathias Mar 18 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 at 12:09
  • $\begingroup$ @Stiv; fixed, tnx. $\endgroup$ – JMP Mar 18 at 12:16

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.