Another faceless jigsaw

Question

Start with a square. Any side of the square can be either straight or have an interlocking pattern, as shown in the two examples below:

That gives $2 \times 2 \times 2 \times 2 = 16$ possible squares.

Is it possible to create a $4 \times 4$ jigsaw puzzle (outside borders straight) with these $16$ pieces? Rotation or flipping of pieces is not allowed.

score 10 · Answer 1 · answered Feb 25 '20 at 21:55

10

Here is an alternative solution that has a bit more structure to it:

+---+---+---+---+
|   %   %   |   |
+-%-+-%-+-%-+-%-+
|   %   %   |   |
+-%-+-%-+-%-+-%-+
|   %   %   |   |
+---+---+---+---+
|   %   %   |   |
+---+---+---+---+
Looking at the 5 horizontal lines, there are 4 adjacent pairs, and each combination occurs exactly once. The same goes for the vertical lines. Therefore all the tiles are different, and every combination of four sides occurs exactly once.

answered Feb 25 '20 at 21:55

Jaap Scherphuis

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+1 cus it makes my OCD feel warm and fuzzy – TCooper Feb 26 '20 at 03:29
Very cool. Looks a whole lot nicer than mine! – hagfy Feb 27 '20 at 13:04

score 8 · Accepted Answer · answered Feb 25 '20 at 19:18

8

I think this has them all:

+---+---+---+---+
| 2 % 3 % 2 | 1 |
+-%-+-%-+-%-+-%-+
| 3 % 4 % 3 % 3 |
+-%-+-%-+---+-%-+
| 2 % 2 | 0 | 2 |
+---+---+---+-%-+
| 1 % 2 % 1 | 1 |
+---+---+---+---+

I went with % for the interlocking pattern sides, and the number is how many of those sides a given square has.

answered Feb 25 '20 at 19:18

hagfy

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Wow, that was fast. Well done! – Jens Feb 25 '20 at 21:21

Another faceless jigsaw

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