The numbers on my "Drive Ya Nuts" are as follows (starting from 1 and reading
clockwise: 123456, 143652, 162453, 164253, 165432, 165324, and 146235. As you
can see, each "nut" is unique.
There are several related puzzles, including:
"Japanese Mind Bender", which is logically identical to "Drive Ya Nuts", e
except it used colors instead of numbers, and each hexagon looks like a small
"Super Dominos", 4x6 squares, each divided diagonally into four sections, and
colored in all possible ways with 3 colors (yellow, orange, and brown). Object
is to arrange the squares in a 4x6 array, with adjacent edges of matching
colors, and the border to be only one color. It claims there are about
12000 different solutions, a computer generated number. I find it difficult to
find even one.
"Colored Squares Puzzle", A magnetic version of Super Dominos. They also
suggest a second puzzle as above, but with 2 colors around the edge.
"Colored Triangles Puzzle", also magnetic (a match for "Colored Squares"),
this one has the 3 colors on 24 triangles, arranged in a hexagon. Same problem,
"Try Nine" is octagonal pieces with numbers (similar to "Drive Ya Nuts"),
to be arranged in a 3x3 lattice such that numbers match vertically, horizontally
, and diagonally. That is, the square spaces between the octagons have opposite
edges with the same number.
"Square Crazy" or "Le Carre fou! fou!", a new puzzle from Montreal (If
anyone wants one, I can give you the address). It is 9 cardboard square
"cards", each of which has half a fish on each edge (either the head or the
tail), and each fish is one of 3 or 4 colors. So direction and color has to
match up at each edge of the 3x3 square. I met the inventer, and he says
he used a computer to ensure there is only one solution.
"Its Knot Easy" has 16 square plastic pieces to be arranged in a 4x4 array,
so that the picture of a rope running through the pieces forms a continuous loop.
And many more. Including a dodecahedron whose faces turn, to try to get a
continuous loop running through it, and a version of 3x3 squares which uses
heights instead of colors.
I think all the "Instant Insanity" type of puzzles are also related to this.
What we need are some non trial-and-error methods of solution, as well as
algorithms to tell if the solution is unique.
By the way, I am planning to make a Rubik's cube with 9 colors, with a
solution having 9 different colors on each face. The question is, how to
design it so it is solvable (preferably not just by trial-and-error), and
so there is a unique solution.
--- Stan Isaacs