# Getting all same side pairs

The goal is to get same side pairs of the 6 tiles,

,

to fit into a $2\times 3$ grid, so that all touching sides match like so (excluding the red part), for example:

• Are we allowed to rotate the tiles? Also, is 2x3 two wide or three wide? – boboquack Aug 29 '17 at 8:32
• You can rotate, and if you can rotate, whether it's $2\times 3$ or $3\times 2$ doesn't matter. – user39732 Aug 29 '17 at 9:17
• did you make the example up? – JMP Aug 29 '17 at 9:38
• is the answer unique? can you flip tiles? – JMP Aug 29 '17 at 10:36
• This is also known as tetravex. – EKons Aug 29 '17 at 16:12

3 solutions i found, no idea if there are others

• Dang, but I gotta say: If the solution is not unique, what's the point? I feel like the puzzle suddenly has much less value since little effort is actually needed to construct such puzzles... – greenturtle3141 Aug 29 '17 at 21:25

I found this by hand. I don't know if this solution is unique.

     4   2
1 X 5 X 5
2   6
6 X 3 X 1
5   2
1 X 1 X 3
4   4

I'll draw a picture of it later.

• why do i even try – Jan Ivan Aug 29 '17 at 11:08
• @JanIvan Sorry I just beat you to it. It is interesting that you found the same solution as I did. Maybe it really is unique. – Jaap Scherphuis Aug 29 '17 at 11:10
• Yea found second, and it is very similar honestly – Jan Ivan Aug 29 '17 at 11:19

There are exactly

8 solutions, or if we don't count rotations, the answer is 4 solutions, or if we count $3\times 2$ table, 16 solutions.

solutions!

How did I find them?

Programming :P

Where are the solutions?

And?

And??

• Rather than saying "I solved it, I'll edit my post soon with the answer", please just post the answer first time around – Joe Aug 29 '17 at 14:11
• Only 4 if you don't count rotations. – Kruga Aug 29 '17 at 14:47
• Yes but we're allowed to rotate. – MCCCS Aug 29 '17 at 14:48
• In that case there are 16, since you can also rotate 90 degrees. – Kruga Aug 29 '17 at 14:50
• Yep. It is. My fault. – MCCCS Aug 29 '17 at 14:53