Wednesday, August 31, 2022

A Tray Too Big – Jigsaw 16

Jigsaw 16 by Yuu Asaka
Jigsaw 16 reminds me of the children’s toy where you have to fit the correct blocks in the matching holes.  To make it easier, the holes are bigger than the blocks!  And to make it even easier, the pieces can also be placed within more than 1 hole!  How long could it possibly take to fit the 16 puzzle pieces into the 16 puzzle piece holes?

Jigsaw 16 is a 2D packing puzzle designed by Yuu Asaka, who has developed a series of jigsaw puzzles, each with their own twist.  The puzzle is made from laser-cut acrylic.  It comes with a white tray consisting of 16 recessed areas in the shape of jigsaw puzzle pieces and 16 blue jigsaw puzzle pieces that have to be placed within the recessed areas.  Of course, you will quickly discover that the recessed areas are a bit too generous and support the placement of more than one piece.  And no - the additional space added to the recessed areas wasn’t meant to aid your attempts at placing pieces - BwaHaHaHaHa!

Jigsaw 16 Box
I started working on this puzzle as a fidget toy whilst on the phone.  Starting with what looked like the hardest to place pieces, one-by-one I would try to place them in the tray.  If there was no available spot, I tried to find an occupied spot that it would fit into and then find a place for the newly evicted piece.  I eventually realized that I was going around in circles and that I had to energize some brain cells to focus on the problem.  

Having lost its fidget toy status (sorry to whomever I hung up on), it now required some mental tracking of where the pieces could possibly be placed and then finding a placement where there is no overlap.  This is basically an exact cover problem for the piece placements.  Although it would probably be easier to create a matrix of piece and viable hole matches to select the exact cover, that would defeat the purpose of converting the math problem into a puzzle.

So, I continued to attack the puzzle as … a puzzle.  The solve was broken into 3 main stages.  Place the most finicky pieces first (the ones with 2 prongs on adjacent sides).  Once those 6 pieces were in place, I tackled the other 5 finicky ones with 2 knobs on opposite sides, which required bumping some of the pieces of the original set.  With all the finicky pieces out of the way, I expected the rest to fall in place without much of a fight.  Although the next 6 1-tab pieces were easier to place, it did require bumping some of the finicky pieces.   In case you haven’t noticed, there are various accepted labels for the male bits of puzzle pieces.  The final, decidedly feminine, piece was then added.

Jigsaw 16 Directions
The most difficult part of Jigsaw 16 is figuring out that there is a second challenge.  It’s not mentioned anywhere, but a picture on the back of the packaging shows some of the pieces connected to each other.  It turns out that the 16 pieces can be assembled into a square.  Please feel free to laugh here, but I thought that this would be easy.  It’s no easier than placing the pieces in the tray.  In fact, its comical seeing how 15 pieces can be joined leaving a space that doesn’t match the final piece.  After much backtracking, I finally had a complete square.

For me, both challenges of Jigsaw 16 fell into the grind-it-out category.  I didn’t find an elegant method to solve this puzzle but I was very impressed with the design.  Especially since it had 2 difficult challenges.