Box Puzzle Notes on Investigation

(1) There are 51 possible shapes. Here 36 shapes are shown.

Those with a * also have a reflection.

These extra 15 reflections makes the total 51.

The solutions have been shown in sets.

A set of nine generated with both boxes

flat and one on top of the other.

Reflections exist for five of these (marked with *).

Here for example is the reflection of the last piece.

Investigation (2)

4 Box Cuboids

These non congruent pairs join to make cuboids.

(3)6 Box Cuboids

Here are two solutions. There are others.

There are of course also the solutions in 6 Box Puzzle (A) and (B)

One approach to creating puzzles is to build a cuboid with 6 loose boxes

and then see how the boxes could be glued. There are two cuboids worth

investigating, as shown in theses examples, one with sides in the ratio 2:3:6

and the other in the ratio 3:3:4

For example start with the arrangement used in the 6 Box Puzzle (B)

and you will find that here are variety of ways the boxes can be paired: