# Unknown 5-pieces cube puzzle - help recognize

I have strange 5-pieces cube puzzle which I can't solve for a long time. I don't know name of the puzzle and can't google it. I'm not sure that there are all pieces. Can you help to recognize it?

Update: Thank you for you answers. It's really must be 6 pieces.

I finally found site with 3d model for download and printing it And its name Printable Interlocking Puzzle #2

I haven't seen this puzzle before. I cannot tell you the name or who produced it.

But assuming your goal is to reassemble it, I can help.

It seems the problem is to fit all 5 pieces in a 4x4x4 cube. In the solution there are visible holes left.

Edit: As Weather Vane noted, a missing 6th piece can complete the puzzle. The goal was to build a solid 4x4x4 cube with the 6 pieces.

Here is the solution:

There are exactly 2 ways to fit the pieces in a 4x4x4 cube.
Each letter A-E is a piece, the 4 squares represent le layers from bottom to top.

| C B E C | C C C C | . A A A | . B E E |
| B B E C | C B E C | . B E A | . B E . |
| B B D D | C . D C | A B D A | . B D A |
| . C D . | C C . . | A A A A | A B D D |
| . B C E | . . C C | . A A A | . . . . |
| . B E E | C B E C | . . E A | B B E E |
| C B D D | C B D C | A B D A | B B D A |
| C B D C | C C C C | A A A A | A B D D |
The first way is interlocked in such a way that no piece can move.

The second way not only can be disassembled, but additionally the empty space is all in one piece. It can be filled by a missing 6th piece to complete the 4x4x4 cube. Weather Vane made a nice picture of it.

And here is how to (dis)assemble it.

Note: +x is right, +y is down, z+ is up a level.
The first move is to remove the now missing piece, sliding it left.

start

| . . . . . . | . . . . . . | . . . . . . | . . . . . . | . . . . . . |
| . . . . . . | . F B C E . | . F F C C . | . F A A A . | . F F F F . |
| . . . . . . | . F B E E . | . C B E C . | . F F E A . | . B B E E . |
| . . . . . . | . C B D D . | . C B D C . | . A B D A . | . B B D A . |
| . . . . . . | . C B D C . | . C C C C . | . A A A A . | . A B D D . |
removed F:-x
| . . . . . . | . . . . . . | . . . . . . | . . . . . . | . . . . . . |
| . . . . . . | . . B C E . | . . . C C . | . . A A A . | . . . . . . |
| . . . . . . | . . B E E . | . C B E C . | . . . E A . | . B B E E . |
| . . . . . . | . C B D D . | . C B D C . | . A B D A . | . B B D A . |
| . . . . . . | . C B D C . | . C C C C . | . A A A A . | . A B D D . |
moved B:-y
| . . . . . . | . . B . . . | . . . . . . | . . . . . . | . . . . . . |
| . . . . . . | . . B C E . | . . B C C . | . . A A A . | . B B . . . |
| . . . . . . | . . B E E . | . C B E C . | . . B E A . | . B B E E . |
| . . . . . . | . C B D D . | . C . D C . | . A . D A . | . . B D A . |
| . . . . . . | . C . D C . | . C C C C . | . A A A A . | . A . D D . |
moved A:+x
| . . . . . . | . . B . . . | . . . . . . | . . . . . . | . . . . . . |
| . . . . . . | . . B C E . | . . B C C . | . . . A A A | . B B . . . |
| . . . . . . | . . B E E . | . C B E C . | . . B E . A | . B B E E . |
| . . . . . . | . C B D D . | . C . D C . | . . A D . A | . . B D . A |
| . . . . . . | . C . D C . | . C C C C . | . . A A A A | . . A D D . |
removed B:-y
| . . . . . . | . . . . . . | . . . . . . | . . . . . . | . . . . . . |
| . . . . . . | . . . C E . | . . . C C . | . . . A A A | . . . . . . |
| . . . . . . | . . . E E . | . C . E C . | . . . E . A | . . . E E . |
| . . . . . . | . C . D D . | . C . D C . | . . A D . A | . . . D . A |
| . . . . . . | . C . D C . | . C C C C . | . . A A A A | . . A D D . |
moved E:-z
| . . . . . . | . . . . . . | . . . . . . | . . . . . . | . . . . . . |
| . . . . E . | . . . C . . | . . . C C . | . . . A A A | . . . . . . |
| . . . E E . | . . . E . . | . C . E C . | . . . E E A | . . . . . . |
| . . . . . . | . C . D D . | . C . D C . | . . A D . A | . . . D . A |
| . . . . . . | . C . D C . | . C C C C . | . . A A A A | . . A D D . |
moved C:+x
| . . . . . . | . . . . . . | . . . . . . | . . . . . . | . . . . . . |
| . . . . E . | . . . . C . | . . . . C C | . . . A A A | . . . . . . |
| . . . E E . | . . . E . . | . . C E . C | . . . E E A | . . . . . . |
| . . . . . . | . . C D D . | . . C D . C | . . A D . A | . . . D . A |
| . . . . . . | . . C D . C | . . C C C C | . . A A A A | . . A D D . |
removed E:-z
| . . . . . . | . . . . . . | . . . . . . | . . . . . . | . . . . . . |
| . . . . . . | . . . . C . | . . . . C C | . . . A A A | . . . . . . |
| . . . . . . | . . . . . . | . . C . . C | . . . . . A | . . . . . . |
| . . . . . . | . . C D D . | . . C D . C | . . A D . A | . . . D . A |
| . . . . . . | . . C D . C | . . C C C C | . . A A A A | . . A D D . |

From there it is obvious. You can move D out, A and C are not interlocked.

To assemble the puzzle, reverse the steps.

• Are these the same A to E labels as I used in my answer? Can either of the arrangements use a single whole sixth piece to fill the 11 gaps in each? – Weather Vane May 19 at 18:48
• Actually, I did not refer to your answer when I named my pieces. Using your colors, I have A red, B green, C yellow, D purple, E blue. An extra E mark was a mistake from an early version of the program. I fixed it. Hopefully it is correct now. – Florian F May 19 at 18:52
• Excellent remark! The empty space is connex in the second arrangement. It can slide out as a first move. This means the puzzle was probably a full 4x4x4 cube and could also explain how the piece got lost in the first place. – Florian F May 19 at 18:59
• I searched the arrangements with a program. If it is correct, this is the only solution. The other is not doable. I also used a program to check what piece can move. I chose the moves by hand. – Florian F May 19 at 19:50
• I have added a construction of the missing piece you found to my answer. If it is correct, please feel free to add it to your answer, if you want to, and edit mine to remove it. It was your solution, not mine. – Weather Vane May 19 at 20:17

Following the excellent answer from @FlorianF here is a set of images showing his missing piece (four angles). This is Florian's solution, not mine, I just added a graphic.

(Earlier)
I have not seen this exact puzzle. I wondered if it is complete.

Assuming the pieces form a hollow cube size 4 x 4 and labelling them as shown:

The number of sub-cubes should be $$4^3 - 2^3 = 64 - 8 = 56$$
Counting the sub-cubes in each piece:
A 12
B 12
C 7
D 8
E 14
but their sum is only $$53$$.

So is there a 3-unit piece missing, or a hole/holes in the completed puzzle?
Or, is there a 11-unit piece missing, with the result being a solid cube?

Edit:

Labelling the pieces by colour

A Red
B Green
C Blue
D Purple
E Yellow

Let's start with the E-Yellow as the base, and try to place A-Red. You can see that the only place for A-Red is the upper face. It will almost go on the right-hand side face, but one prong is in the way.

Now let's look at B-Green. It can't go as the top face, because A-Red will be there. There is one side position it can occupy, like this.

But how can A-Red now go at the top? It can't.

So I am as mystified as ever by the puzzle, but perhaps the centre must be filled too.