# Tiling with Js and Ls

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.

## 4 Answers

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

And if the pattern isn't obvious:

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

• It's my turn to be impressed! Commented Sep 16, 2021 at 19:30

UPDATE Down to 6 outcolour tiles

Here is one way:

original pair of tiles is marked by black boundary.

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

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

• I think you are keeping the wrong colours. Perhaps your answer may even get simpler if you fix that? Commented Sep 12, 2021 at 15:02
• 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.
– Bass
Commented Sep 12, 2021 at 15:21

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

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.

• 10 outcolor tiles apparently, for posterity Commented Sep 13, 2021 at 6:17