Myopic Doves

Variations

Rick Eason

Top view of all possible Myopic Doves type pieces

Note that the piece labeling has changed from the main Myopic Doves page in order to represent all pieces in a systematic way

In each case the tail is on top

Note that piece "A" has the grove intersecting the notch, so it will not be used.

A file giving all possible sets of pieces that will assemble is given here.

The most challenging puzzles are likely those having a piece set that will pack in the most number of ways,
only one of which will actually disassemble. Some might say it has a single solution and a number of "false
solutions." When working such puzzles you will likely arrive at a one of the "false solutions" thinking
"this last piece certainly goes here" but there is no way for it to actually get into position.

One will note from the table that some of the piece sets will pack in 33 different ways or 18 different ways,
only one of which will assemble/disassemble; however an examination of these puzzles will reveal that the "false solutions"
of these piece sets involve packing the pieces in two complete layers with no tails or notches shared between them,
(assuming they could assemble) and then making 16 trivial rearrangements of these two layers. The puzzles with 32
"false solutions" and one real solution (33 total) each have two ways to make two such layers, and the puzzles with
17 "false solutions" and one real solution (18 total) have one way to make two such layers, and one false
solution without layers (and no trivial rearrangements). I therefore consider such piece sets as having only two
actual false solutions.
From the table, the "best" puzzles are those with four ways to pack and a single solution.

With the above labeling the "Official Myopic Doves" are given by piece set "BCDEIJKN"
(and the mirror image puzzle is given by the piece set BCDHIKLM). This particular puzzle has four ways that the
pieces will pack into a cube, but only one of these ways will actually assemble/disassemble. Two other sets of
pieces that will pack in four ways, only one of which will assemble/disassemble are given by the sets
BCEGHIKM and BDFIJKLN.
(The mirror image sets of these two sets are CDEIKMNO and BDHIJKLP, respectively.)

We can define the "dual" of a piece as the piece which results in swapping the tail and the groove, and the dual of
a puzzle as the puzzle which results from swapping all pieces with their duals. In the above piece sets, we find
that the set BCEGHIKM is the "dual" of the "official Myopic Dove" set, BCDEIJKN. It turns out that the dual of the set
BDFIJKLN, which is CEFGHKMO, has four solutions which pack (as expected), but all four of these packings will disassemble.

© Richard Eason, 2004