# need help in solving burr or cube puzzle

I have a 8 piece wooden puzzle that I found in a yard sale that I can not figure out. All pieces are the same thickness.

Thanks for all help.

Sorry about the last post, new here and not sure how all this works.

Thanks for all the ideas from everyone. The person I bought this from swore that it was just one puzzle and made a cube.

The only way I was able to make a cube was by loosely stacking the blocks on top of one another, but then this does not hold together, and then why the notched pieces?

• Hey! It would be better if you edit your old question, and add this image there instead of posting a new one as it can be considered as a duplicate of the previous one. Happy Puzzling! – Eagle Jul 17 '19 at 16:57
• Has a useful answer been given? If so, please don't forget to $\color{green}{\checkmark \small\text{Accept}}$ it :) – Rubio Jul 20 '19 at 5:56

If we call the common height of all these pieces one unit, then collectively they contain 24 cubic units' worth of stuff. So we might expect that they form a cuboidal block of size, let's say, 2x3x4 units. But I think this is impossible!

Let me introduce a bit of notation. Suppose the block we're trying to build is $$l\times m\times n$$ units in size. Call the things there are $$2l\times 2m\times 2n$$ of "cubies", the things there are $$l\times m\times n$$ of "cubelets", and the whole thing the "block". Say that two cubies are "of the same type" when they occupy corresponding spaces in two cubelets. (So there are 8 "types" of cubie in the block, 24 of each type.)

Now, five of those eight pieces are made out of 2x2x2 units, which means that wherever you place any of them in the block they will have equal numbers of cubies of each type. The whole block, of course, also has equal numbers of cubies of each type. So when we place the three remaining pieces -- the ones with parts just one cubie in thickness -- they too must, taken together, have equal numbers of cubies of each type.

Two of those three pieces are the same. Wherever you place one of these, it will contribute 1 cubie of each of four types and 3 of each of the other four types. In particular, it will contribute an odd number of cubies of each type, and between them these two pieces will contribute an even number of cubies of each type.

So, no matter how we place the seven pieces we've considered so far, the number of cubies of each type will have the same parity: all odd, or all even. So we must place the last piece so that it too contributes equal-parity numbers of cubies of each type (since in the completed block we have equal numbers of each type of cubie).

But this can't be done! That piece provides 1 each of two types of cubie, 3 each of two types of cubie, and 2 each of the other four types of cubie. (Exactly which types are which depends on where and how you place the piece.)

So, I think at least one of the following things has to be true.

• The shape these pieces are meant to go together to make isn't a block whose sides are all integer multiples of one "unit" with no gaps.
• They go together in some super-weird fashion where they are at non-right angles or non-"integer" positions or something. (This seems obviously impossible, but maybe my intuition is broken.)
• They aren't actually the right set of pieces; there are some more, or some of these are from a different puzzle and just happen to look like they're the right size for this one, or something.
• The puzzle is some sort of a hoax or trick, impossible by design.
• There is some boneheaded mistake in my analysis above.

One kinda-plausible possibility is that they form a 3x3x3 cube with some gaps (and part of the challenge will presumably be to assemble things in the right order, which will need some burr-puzzle-style sliding around). Another, mentioned by Jaap Scherphuis in comments, is that these are actually pieces from two separate puzzles (probably made by the same people since the pieces are so similar).

• I reckon these are part of two puzzles - one burr puzzle and one cube-shaped block puzzle. The puzzles look like a they form a series from the same maker. – Jaap Scherphuis Jul 17 '19 at 19:00
• That seems possible. They certainly seem similar enough that it's unlikely they're from two entirely independent puzzles. – Gareth McCaughan Jul 17 '19 at 19:03
• Wait, I've miscounted something, haven't I? There are 24, not 27, cubelets' worth of stuff in these pieces. – Gareth McCaughan Jul 17 '19 at 19:05
• So maybe they form a 2x3x4 block instead, or maybe they form a 3x3x3 cube with some gaps inside. – Gareth McCaughan Jul 17 '19 at 19:05
• Er, the 2x3x4 block is of course impossible. – Gareth McCaughan Jul 17 '19 at 19:05

I think I have found out what the two puzzle are to which these pieces belong.

The middle four pieces are part of a fairly standard burr puzzle, i.e. a puzzle which when solved has three pairs of parallel pieces intersecting each other to form a kind of three dimensional cross shape. Of the four pieces you have, the fourth is the unique key piece that is inserted last. I believe that the two pieces you are missing are one of each of the other two types of piece you have (though instead of another copy of the first two pieces you could have a similar piece with a block in the middle, i.e. with just two slots). The best picture I've found is from this site, though it uses slightly longer pieces:

You can see other versions of this puzzle on Jim Storer's site.

The other four pieces are from the "Diabolical Cube". It was described in the 1893 book Puzzles Old and New by Prof Hoffmann. The puzzle has 6 pieces of sizes 2, 3, 4, 5, 6, and 7. You are missing the pieces of size 5 and 7. This site has the following nice picture of the pieces:

Taking the smallest indigo piece, on the left, to be 2 units, the volume of the eight pieces is 24. So to make a solid cube of volume 27 units, there would either be a piece missing (volume 3) or there is a cavity inside after the manipulation of pieces.

Can it be an interlocking puzzle?
Let's consider the largest piece, the red 6-unit one on the right.
There are two positions where it can go (subject to reflection and rotation):
a) A face. Clearly there is no way that piece can be gripped or trapped by another.
b) A centre slice. Now it does seem possible (somehow), because of the U-shaped pieces.

With b) let's consider how the next largest piece, the square yellow 4-unit one, can fit.
There are three positions where it can go (subject to reflection and rotation):
c) Flat against the first piece. This puts it on a cube face, where it can't be trapped.
d) In an angle of the first piece. This too puts it on a face of the cube.
e) Ditto, but offset by half a unit. It's possible for this to be gripped by a U-piece.

With e) although it is possible to grip with a U-piece, the lugs will only extend a half unit, leaving gaps that can't be filled.

The three jagged pieces in the centre of the OP's shot remind me of a wooden puzzle we had, but there were two of the yellow piece. If that is the missing piece, its volume 2 units would still leave 1 unit short of a solid cube. The two U-shaped pieces have a "tell" – you can see the markings where they have been slid against another piece, which is 1 unit wide, leaving a half unit gap between the lugs. But the only piece which could fit is the yellow jagged piece of which there is only one, where at least 2 half-size pieces are needed.

The five other regular cuboid pieces don't seem to be the same style. In the OP's pictures, they seem to stack nicely into a 3 x 3 x 2 cuboid.

So my conclusion is the same as that of @JaapScherphuisbut, and @GarethMcCaughan but for slightly different reasons: It is a mixture of two incomplete puzzles from the same manufacturer, but intended for different ages. The simple block one is for very young children, perhaps also incomplete.