Two interesting related puzzle ideas. Both are make a cube from the provided tetris like pieces. The wooden one is 3D, the foam one is based on 2D pieces which form a 3D shape.

Foam Puzzle

Lets start with the foam puzzle. First get some high density foam. Cut it with a sharp box knife using slow strokes while pulling the foam gently apart.

2cm thick was the stuff I was using. That means your teeth need to be 2x2x2cm so you get a nice square fit. I created every possible block where you had a 3 by 3 centre and then variable teeth around the outside. The idea was to play with different sets of blocks to find ones which can form a cube, and could make a rectangle when layed flat. Thats my excuse for the untidy cutting - if you are careful you can actually make a pretty neat job.

To save lots of trial and error - a tip is that the total number of teeth used to form a cube is 42.. actually it's 44 but it was close. (e.g. thats the number of blocks if you count the leading edges)

I have also made a giant cube puzzle which is 4x4 pieces on each side - it's an extra challenge to make it lay flat!

Magnet Puzzle

Made famous by the soma cube, wooden 3d puzzles like this are pretty common. A quick computer program and you can work out the pieces required to make puzzles using 4 and 5 cube pieces, 3d or 2d.

The goal here was to come up with a set of pieces which had many solutions, normally you want the least - but here we want to torture people into thinking it's solved.

I made up a set of pieces by cutting up square dowel and gluing them with PVA. I did a bit of iteration until I had a set I was happy with.

Now the secret to the puzzle, use a drill press to make holes just deep enough for ferrite or iridium disc magnets to be glued - remember the two polarities. The plan is to put these in a number of places, some just to throw people off the scent, others to reject alternative solutions.

It's somehow satisfying to watch someone put the last piece in place only to have the magnet throw the piece out of place when they remove their thumb.