Neil's Puzzle Building Blog
17Dec/110

Tromino Trails

This entry is part 5 of 6 in the series IPP 31

Carrying on with my review of IPP31 puzzles, here's another of the puzzles that I picked up when I was at the recent Post IPP California Puzzle Party. Tromino Trails was Stan Isaacs exchange puzzle from IPP31, and given that Stan was the host of the Puzzle party, it would have been rude not to buy one of his puzzles.

Tromino Trails

Tromino Trails

Tromino trails is designed by Donald Knuth and made by Pavels Puzzles. You can read Pavel's description about the puzzle by following the link, and also purchase a copy for yourself if you'd like one. And I highly recommend you do!

This puzzle goes back to 2009, and IPP29 in San Francisco. There Donald Knuth gave a talk about varying puzzles he was working on and passed out a sheet with some puzzle problems that people could play with later. One of those problems was the Tromino Trails problem. I'll let you read about it on Pavel's site, as he was there and will explain it far better than I.

However I digress.The Tromino Trails puzzle is a physical version of Don's paper problem from IPP29. The puzzle consists of 24 L shaped trominoes with varying paths marked on them, a tray that can be configured to a number of different sizes and five challenges.

The first problem, a 6x6 loop

The first problem, a 6x6 loop

You start off with a 6x6 square, and 12 pieces, with the goal being to fit the pieces into the tray and form an unbroken loop with the trail marked on the pieces. There's a single unique solution to the problem. Given that the tiles are transparent, the trail is visible on both sides, and therefor can be flipped over and rotated as desired.

The 6x8 challenge and pieces marked with one dot.

The 6x8 challenge and pieces marked with one dot.

You then move a few bars around and get a larger 6x8 tray, add four marked pieces, and have the same goal of an unbroken loop. Again this problem has a unique solution.

Reconfiguring the tray to the next size

Reconfiguring the tray to the next size

Moving the tray around is easy as the spacers all have tabs on their ends that fit into notches in the tray and have a number of dots based on the challenge you're attempting. A great idea and really well thought out.

Next up a 6x9 tray created by moving more black frame pieces, and two new trominoes. Same goal, same unique solution ... are you seeing a pattern yet?

All five challenges, add progressively more pieces, and a bigger tray until you're using all 24 trominoes, all with unique solutions, and you have a beautiful, and elegant puzzle design. I think the nicest thing about this (given that we know I'm not good at tray packing puzzles) is that this one is really approachable. I've been able to solve all five problems, and none of them are too difficult. Yes they're a challenge, but not such that you get frustrated and want to throw the puzzle across the room.

There's no solutions provided, but if you are stuck, or just curious, then click the 6x6 solution link or the 6x8 solution link to see the solutions. After that you're on your own. After all, what's the point in my giving you the solution. This is actually a fun tray puzzle!

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