ABSTRACT
All of the puzzles described thus far have been non-interlocking. Most of them employ a tray or box to hold the pieces in place. The puzzles to be described in this chapter, and throughout most of the remaining chapters, are interlocking. In other words, they hold themselves together. To be more precise, an interlocking puzzle is here defi ned as one in which the last step of assembly (or fi rst step of disassembly) necessarily involves the sliding of mating surfaces parallel to each other. Such puzzles tend not to come apart without deliberate effort. A box is no longer needed to hold them, so they can be any geometric shape and can be displayed in full view when assembled. There is more freedom in the manipulation of the pieces. Beyond these obvious practical advantages, isn’t there something intrinsically more satisfying in things that stay together rather than fall apart by themselves? (Anyone who owns a car like mine will understand!)
Cubic Block Puzzles The polycube pieces in the previous chapter were formed by joining cubic blocks together in different ways. None of the pieces thus formed up to size-fi ve are suffi ciently crooked to have much practical use as interlocking puzzle pieces. More important, 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 3 × 3 × 3 cubic solid is an obvious place to start, with its thousands 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. By defi nition, an ideal combinatorial puzzle is one in which all pieces are dissimilar and non-symmetrical. A four-piece dissection of the 3 × 3 × 3 cube that achieves this is shown in Figure 73. The puzzle is serially interlocking, meaning that it can be assembled in one order only.
