3 Pentagons

This past weekend, I played with Japanese puzzler/designer Koshi Arai's 3 Pentagons. The object of the puzzle is to lay the pentagon shaped (5 sided) pieces on a flat surface and form a symmetric shape. 

For this puzzle, there were not one but three solutions and Koshi had in fact (generously) shown one of the symmetric shape solutions on the instructions that came with the puzzle. The task is figuring out the remaining two. 

This is the 1st symmetrical shape solution provided by Koahi Arai

3 Pentagons was not only Koshi's IPP34 Exchange Puzzle but he also entered it for the Puzzle Design competition. His exchange version is finely made of an exotic (dark) wood (cocobolo?) and all the pieces precisely cut. 

Unless you know the meaning of "symmetrical shape", you won't even know where to begin. There are typically two types of symmetrical shapes possible, one is mirror or line symmetry and the other is rotational symmetry. In most (if not all) of these symmetrical shape type puzzles, usually the object is to find a mirror/line symmetrical shape, which is the case here.

It took me several sessions over two days to find the two solutions. What makes the puzzle so difficult is that the three pieces are pretty similar in shape (and size) to each other and this sets up a huge number of possible combinations for joining the pieces side to side; yet only three symmetrical shapes exist. What an incredible design! I am very sure there is some complicated mathematics to all this but sorry folks, I am not capable of explaining any of it here...all I know is that I tried all sorts of ways to put the pieces together and eventually got the results I wanted.

Overall a very challenging puzzle indeed and a good thing that Koshi revealed one solution at least! If anyone wants to know the other two solution shapes, please contact me via my blog email.

Heptagon 48

The Heptagon 48 is one of the most beautifully made puzzles I have come across. The marble (yes marble!) version of this tray packing puzzle was Japanese designer Koshi Arai's competition entry at the IPP 32 Nob Yoshigahara Puzzle Design Competition held in Washington, USA this August. It was also one of three entries that won a Jury Honourable Mention at the competition.

When I first saw the marble Heptagon 48, I immediately contact Koshi-san for price and availability but the quoted price was a bit too high for me so I decided to settle for his wooden (less expensive) version instead. And I have no regrets buying the latter.

And now to the scientific bits. A heptagon is a polygon with seven sides. Together four heptagons can be joined together at the edges to form a "tetrahept", which in turn become the individual packing pieces of this puzzle. 12 "tetrahepts" consisting of six different designs (making a total of 48 heptagons) make up the pieces required to fill the tray. If you are confused like I am about all this technical stuff, check out Koshi-san's website where he has loads more information about his puzzle and Heptagons.

This puzzle is made of two different woods. Both the individual pieces and tray are made of dark rosewood for the top surfaces and light coloured birdseye maple for the bottom. The tray measures about 17cm x 13cm x 2cm. Quality of construction is excellent with incredible finishing. All the individual pieces have been (laser?) cut to very tight tolerances and fit just nicely with each other into the tray. This puzzle even comes in a nice beige gift box.

The object of the puzzle of course is to fit the 12 tetrahepts into the tray with all the pieces dark side up. The puzzle comes to you partially solved with 2 tetrahepts wrong side up (ie light pieces facing up). The tetrahepts do not cover the entire tray, even when correctly packed in, but will leave "pentagonal" spaces in between, which is intended.

According to Koshi-san, there are an unknown possible number of solutions, of which he has discovered 57 to-date; all with a combination of dark and light pieces facing up but only two that have all pieces dark (correct) side up. So far all my attempts have yielded only one solution; ie one remaining piece that can only be inserted but wrong side up. I only managed to solve the puzzle properly when Koshi-san sent me his 57 solutions in PDF.

The Heptagon 48 is very challenging.  There are no straight edges; all the 4 sides of the parallelogram-shaped tray cavity are "jagged" to fit the tetrahepts. You have to grapple with pieces that not only look geometrically similar, but work with the same dark coloured woods for both the pieces and tray, which provide no contrasting reference points to aid in solving. And because the pieces fit so well and closely together, inserting and removing the pieces from the tray is not an easy task either, which makes it all the more difficult.

If you are into tray packing puzzles and want serious quality, well, the Heptagon 48 definitely should not be missed. It is available directly from Koshi Arai via email.