In this puzzle you must tile the plane with identically sized colored L and J tetraminos. To start I will place two of them like so:

Your task will be to tile the entire rest of the plane meeting four conditions

  1. My initial tiles will remain where they are.

  2. No two tetraminos of the same color can share a side.

  3. All tetraminos must be 1 of three colors (the two colors used already plus one extra)

  4. With a finite number of exceptions, all tetraminos should be one of the two colors initially used. That is to say that you should be able to draw a box such that only these two colors of tetraminos appear outside of the box.

How can this be achieved?

If you want to try an easier version of this, try relaxing rule 3 to allow 4 colors. If you have solved this try minimizing the number of tiles of the third color.


UPDATE Down to 6 outcolour tiles

Here is one way:

![enter image description here
original pair of tiles is marked by black boundary.


Inspired by loopy wait's solution, I improved on it.

Large J and L pattern

And if the pattern isn't obvious:

Same image with white lines cutting the image in regular tiles

Interinstingly, this is the only way to extend the tiling around the center core of 12 pieces without adding any more green piece.

  • $\begingroup$ It's my turn to be impressed! $\endgroup$
    – loopy walt
    Sep 16 at 19:30

This is obviously way too complicated (and also a bit late), but posting anyway:

enter image description here

The square block marked at the lower left can be multiplied to tile the plane; it'll fit itself on all four sides.

  • 1
    $\begingroup$ I think you are keeping the wrong colours. Perhaps your answer may even get simpler if you fix that? $\endgroup$
    – loopy walt
    Sep 12 at 15:02
  • $\begingroup$ Ah, quite possibly. Trivial to fix, of course, since you can just take the complete tiling, draw a box at some point, and change one of the colours outside it. $\endgroup$
    – Bass
    Sep 12 at 15:21

An answer with more symmetry and fewer uses of color 3: [as of posting time, anyway; this answer is now obsolete]

enter image description here
The given region is outlined in yellow - I stumbled across this solution after a few failed attempts when I noticed the nice structure outlined in grey.

  • $\begingroup$ 10 outcolor tiles apparently, for posterity $\endgroup$
    – somebody
    Sep 13 at 6:17

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.