I also considered using Lego like Neil describes on his blog, but as all of my Lego is happily tucked away in my Mum's loft (where it has been for a while) I decided to go for dice.
Dice are brilliant building blocks for projects like this as they are manufactured to consistently be the same size and shape. I managed to assemble these two standard 3x3x3 Soma Cubes using only the dice, some super glue and a solid ruler. I made the black one first, and normally all standard Soma Cubes have 240 distinct solutions, but as all of the numbers on each side match I imagine this number is greatly reduced. It could even have only one solution, but I'd need someone with better Burrtools skills to find that out for me.
The first one went pretty well so I went on to make another, except I designed it with coloured die so that a pattern could be formed on the surface. I love the look of this one, and as well as the pattern all of the sides of the cube are numbered just as a normal die would be.
Now I said that dice are consistently manufactured to the exact same size and shape, but this isn't always entirely true. I attempted to build a burr puzzle which would have been made of over 120 cube units, and each burr piece would've had to be 6 units long. The sides of each die look very flat, but there are slight irregularities. The irregularities are so slight that they really make no difference on my 3x3x3 cubes, but on pieces that are 6 units long the irregularities add up and cause some real alignment issues.
Oh well, my first DIY puzzle attempt went quite well I think, now I shall have to find some better manufactured die to build something a bit more exciting. Watch this space!
I gave a set of my dice cubes to Allard at our last get together, and he has done a little write up for them on his blog. Check it out!
I would guess that your puzzle does now have only one solution, and you may be able to come up with a fairly simple argument for this. Does it make the puzzle a lot easier knowing the die all end up oriented the same? I would think it would.
ReplyDeleteI think that having all of the die in the same orientation does make the puzzle slightly easier in itself, but I reckon it still ends up being more difficult than a standard Soma Cube. I'd need to get a few people to try it out and see what they think.
ReplyDeleteHave you read "The Hidden Secrets of SOMA", a section in Volume 4 of "Winning Ways for your Mathematical Plays"? Their analysis shows that the T shaped piece can only appear with its spine aligned with an edge of the cube. So, I'd start with that piece and then see what further restrictions that places on the two faces sharing that edge ...
ReplyDeleteFunny how something you thought was square turns out not to be. Nice work on the Soma cube. A fun little puzzle and nice and easy to create.
ReplyDeleteI found an online version:
ReplyDeletehttp://www.mathematik.uni-bielefeld.de/~sillke/POLYCUBE/SOMA/cube-secrets
I too have no wood working skills but quite fancy making burr puzzles with Lego as described by Neil. I have had a play using the "puzzle will be played" designs. I have used Bricksmith software to get a brick list and then looked on line to buy some bricks. It looks great but at £40 (and more) to get enough for a decent burr puzzle I think I will wait a while - spending an awful lot on other puzzles just now!
ReplyDeleteThanks for the link George, interesting stuff. I should also add that not every die is facing in the same orientation, there are some die that can face different ways and yet still show the correct outer pattern. I think this makes the puzzle harder, but it's hard for me to judge as I know the solution. I may make a few for a few friends and see how they get on.
ReplyDeleteAha, very clever! The center die can face any direction, and those at the centers of the faces could be rotated ...
ReplyDeleteNow you've got me interested in making one of these. I'll look around for an inexpensive source for accurate dice.