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The polycube pieces in the previous chapter were formed by joining cubic blocks together different ways. None of the pieces thus formed up to size-five are sufficiently crooked to have much practical use as interlocking puzzle pieces. More importantly, the combinatorial approach does not lend itself very well to the design of interlocking block puzzles.
The most obvious method of designing an interlocking cubic block puzzle is to start with the complete pile of blocks, held loosely together by your imagination or some other means, and remove one piece at a time. A 4 x 4 x 4 cubic pile is a good size for this, with its millions of possible dissections. Depending upon just what the objectives are, quite a bit of experimenting may be required to achieve the desired results. Again, the plastic play blocks that snap together are handy.
A commonly accepted rule for combinatorial puzzle design is that the pieces all be dissimilar and non-symmetrical. The fundamentals of good design also require that the simplest possible pieces be used that will do the job. Given the 4 x 4 x 4 cube then, this translates into maximizing the number of pieces. What is the maximum number of dissimilar non-symmetrical pieces that will assemble into an interlocking 4 x 4 x 4 cube? (Answer unknown.)
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