How to create a cube out of uneven sides

Question

We are given:

1. four pieces of wood; each piece is 10 cm long, 10 cm wide, and 2 cm thick
2. two pieces of wood; each piece is 12 cm long, 12 cm wide, and 2 cm thick
3. An 8 oz bottle of wood glue

Provide instructions to assemble a cube from these components. The cube must survive a drop from a height of 10 cm and remain intact.

I want to know is this even possible mathematically without cutting the wood?

Answer 1

You can make a 12x12x14 box.

With the four 10x10x2 pieces glue them together thusly:

+--+----------+
|  |          |
|  +-------+--+
|  |       |  |
|  |       |  |
|  |       |  |
+--+-------+  |
|          |  |
+----------+--+

This makes a 12x12x10 frame (each side is 10+2) Then glue the two 12x12x2 on as end caps for a 12x12x14. I believe this is what Mike Ernest is talking about.

Every glued pair is a 10x2 surface.

If instead you have four 10x8x2, then you get a 12x12x12 cubical box with an 8x8x8 hollow center.