Box Puzzle Investigation

(1) Here is an investigation which provides very good practice in recording

3-dimensional shapes using isometric paper.

Can you find as many different ways as possible that two matchboxes

can be joined together like the pieces in Box Puzzles. This means that

the overlap, the area of contact must be an integral (whole number) of “squares”.

So this is allowed

but this is not.

Record your results on isometric paper. Click here for Isometric Grid

(2) Can you discover which two “pieces” (ie a “piece” is made

from two match boxes) can be combined to make a cuboid ?

For example it is obvious that 2 pieces like this will make a cuboid.

Can you find pairs of non congruent pieces that join to make a cuboid?

(3) Can you create new puzzles using 6 boxes

similar to the 6 Box Puzzles (A) and (B)?

The most interesting puzzles are created when

a) all the pieces are different, non congruent,

b) none of the pieces are made by joining two boxes with congruent faces matched (e.g. the middle piece in the first solution shown).