Four Z's

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(Click to Enlarge)

The puzzle I'm reviewing today is from my favorite type of puzzles... Packing. The Four Z's puzzle is a close relative to the classic 1983 design by Peter Hajek, the Four T's. I didn't find any information about the Z's puzzle, so I'm not entirely sure if it's a Peter Hajek design as well.

The puzzle comes in a classic design box and respective lid and it's made from Samanea Saman wood (or Rain Tree wood). It measures 10x10cm (about 4") with the cover. As the name suggests, the Four Z's consists of four pentominoes in the shape of a 'Z' and you have to pack them in the provided tray. There are two packing problems, but the first one is so easy, it's not even a real challenge, as there are plenty of room to pack the pieces as you wish. It's more like a way to store the pieces, really. However, the interesting part is that the tray is double sided and when you flip it, you're presented with a smaller board. Now this one's truly a puzzle and there's only one solution.

First a couple of facts about the Four Z's Puzzle:
- The total area of the larger tray is 36 square units (6 units in length). Given the fact that each piece is a pentomino (5 units), there will be a total of 16 units left when you pack them all. That's a lot of units and that's why the first challenge  is so simple.
- The total area of the backside tray is just 30.25 units (5.5 units in length), hence not enough room to fit two pieces side by side, which would need 6 units in length in the tray. The new area will only leave 10.25 units left in the board with the four pieces packed.

(Click to Enlarge) - The Backside Tray

Because the smaller board doesn't have a unit length with a natural number, the solution is not at all intuitive and requires an outside of the box thinking. As a collector, I'm used to see all kinds of packing puzzles, and in 2D packing problems there are mainly two types of puzzles - The ones that make use of an entire tray area and don't leave any empty spaces and the ones that very cleverly, do leave some empty spaces. To me, the second type has the best and toughest puzzles.

As I previously solved the Four T's puzzle, although it was a few years ago, I was already expecting the Four Z's to be as equally hard. Indeed it was... It took me almost an hour of constant fiddling with the pieces to finally solve it. I was almost giving up and ready to pack the pieces on the other side and call it a day, when suddenly the last piece fit perfectly with the others. It was a very nice feeling.

This type of puzzles require that you solve them by yourself, as it it's more rewarding when you find the solution without any help. I can give you a hint, though: If you solved the Four T's puzzle, the solution to the Four Z's is very similar. While I wouldn't recommend it if you want to try it for yourself, you can see the solution here.

The Four Z's is available at Brilliant Puzzles for about $9 USD.

Closing Comments:

As a packing puzzle fan, suffice it to say, I loved the Four Z's. It's one of those puzzles that give you a truly satisfying sense of accomplishment and an a-ha moment. The solution is so cleverly implemented that will certainly surprise you when you solve it... That won't happen before you lose some of your patience first, though.

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