An Experiment in Discovery Versus Invention

You, yes you, can help with this one

There’s a general question of what things are canonical discoveries and what are invented. To give some data answering that question, and because I think it’s fun, I set about to answer the question: What is the most difficult 3x3x3 packing puzzle with each number of pieces? The rules are:

• Goal is to pack all the pieces into a 3x3x3. There are no gaps or missing pieces

• Pieces are entirely composed of cubes

• Each number of pieces is a separate challenge

• Monominos (single cube pieces) are allowed

• The puzzle should be as difficult as possible. The definition of ‘difficult’ is left intentionally vague.

The question is: Will different people making answers to these questions come up with any identical designs? I’ve done part of the experiment in that I’ve spent, ahem, some time on coming up with my own designs. It would be very interesting for someone else to come up with their own designs and to compare to see if there are any identical answers.

Don’t look at these if you want to participate in the experiment yourself, but I came up with answers for the 3, 4, 5, 6, 7, 8, 9, 10, and 12 pieces. The allowance of monominos results in the puzzles with more pieces acting like a puzzle with a small number of pieces and a lot of gaps. It may make more sense to optimize for the most difficult puzzle with gaps for each (small) number of pieces. There’s another puzzle found later which is very similar to one of mine but not exactly the same probably for that reason.

If you do this experiment and come up with answers yourself please let me know the results. If not you can of course try solving the puzzles I came up with for fun. They range from fun and reasonably simple to extremely difficult.