Lucky 7The purpose of the game, as with Loyd's Fifteen and Sliders, is to return the counters into their Home position, position they were in before reshuffling. The puzzle consists of several counters placed on two intersecting circles. There are six points of control: the two central counters and the two pairs of counters adjacent to the central ones. In the case of 7 counters, besides the empty counter, these are numbered 1, 7, 3, 4, 5. Clicking on the upper counters induces clockwise rotations. Clicking on the lower counters results in counterclockwise rotations. Left counters rotate the left circle. Right counters rotate the right circle. The middle ones handle the whole set. The empty counter is skipped in all cases. With 7 counters the puzzle is solvable for any starting configuration. You can experiment with this by hitting the Cheat button which swaps the second and the first counters. If the "Cycles" box is checked, a permutation of counters needed to solve the puzzle is displayed. The permutation is presented as a product of cycles.
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