Packing^©

What looks promising is to try putting blocks into the box and when this can not be completed then to learn from the errors and try placing earlier blocks differently.

But this simple strategy does not work for our harder puzzles (5x5x5 1, 5x5x5 2). The reason is that wrong block placements early on prevent a completion at the end when it is not clear what early move needs to be changed. More thinking and a strategy is needed.

For hard problems one can try to break them up into easier sub-problems. In this case one could think about the task to fill not the whole box but one layer, for example, the bottom layer and then the next layer and so on.

Another good strategy is to think about good questions, like:

1. How many slices (not only horizontal layers but also vertical slices) need to be filled?

2. Which blocks are needed to fill one slice?

3. What is the bottleneck in this whole challenge?

4. How do we have to use our available resources (our small blocks) efficiently to fill all slices?

If you have 125 spare dice then take a tape to bundle them to blocks.

Instead of a 5x5x5 box one could use, for example, a shoebox.

If one holds it diagonally then blocks stay where one puts them.

Our interest in packing puzzles was ignited when seeing the wood version of puzzle 5x5x5 1 at a math exhibition. Following the reference to its author, the famous mathematician John Horton Conway we found puzzles 3x3x3 2, 5x5x5 2, and 5x5x5 3 from him.