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The Zoki Game(s)


The zoki game is a set of thirty-four square cards. Each card is white and the edges are marked with stripes: none (white), one blue stripe, two red stripes, or three black stripes. There are seven different ways of labelling the edges of a square with up to four colors: AAAA, AAAB, AABB, ABAB, AABC, ABAC, and ABCD. Zoki uses only the patterns - AAAA(4), AAAB(12), ABAB(6), and ABAC(12). A very nice picture of the zoki cards is on the zoki website.

There are four zoki games played with the set:

Zoki 9
A solitaire game where you try to assemble nine pieces into a 3x3 square with matching edges.
Zoki 16
The 4x4 version of Zoki 9.
Mira 12
A "concentration"-like game.
Yu-go 9
Two player game building a 3x3 square and scoring points.

Zoki is made by Zoki Game Enterprise.

Zoki 9

The solitaire game I have been investigating is Zoki 9. It is played with a subset of twenty-seven cards. (Leave out all the AAAA cards and the ABAB cards that don't have any zero stripe (white) edges.) You pick a random set of nine cards out of the twenty-seven and make a 3x3 square with all of the interior edges matching.

Is the game always solveable? No, pick the (white, blue, white, blue) card and any other eight cards that do not have any blue edges. This set is not solveable because the first card will always have at least one blue edge on the interior of the 3x3 square and their is no other blue edge to match against it.

Is every set of nine cards unique? No, for some sets of cards it is possible to relabel the edges of the cards in a consistent way and end up with a different set of nine cards whose solution(s) are isomorphic to the initial set.

Ignoring unqiueness there are "27 choose 9" ways of picking a set of nine cards - for a total of 4,686,825 sets. I wrote a computer program to relabel card edges to look for unique sets. I found 435,331 distinct sets.

I modified my program to also test for solutions. I found 430,396 solveable sets out of the distinct sets. Lately I have been trying to characterize the unsolveable sets. For example, there are 463 distinct sets of the form described above - one piece with two (or three) identical edges and no other pieces having that edge color. So far, I have identified three general kinds of non-solveable sets, but I still have slightly over five hundred sets that are not characterized.

Last Updated: 1999-08-04