The Cole puzzle

• The goal of this puzzle is to unscramble the \(3\times 3\) boxes by applying a sequence of permutations. First, pick a permutation group on the left-hand panel. Theoretical information on the selected group is given above. The bigger the group, the harder the challenge.
• The buttons underneath the grid perform fixed permutations as indicated by their icon. Clicking with the right mouse button performs the inverse permutation (i.e. undoes the left button click).
• The middle button under the grid can be defined as a combination of the left and right buttons. To set this up, right-click on the middle button and enter a sequence of L, L', R and R' without spaces or commas. Here, L and R denote the left and right buttons, and L' and R' denote the respective inverse actions.
• For convenience, the buttons can also be executed on the keyboard (left, up and right arrow keys; combine with ctrl for the inverses).
• Once you're familiar with the controls, press Scramble and try to solve the puzzle in as few moves as possible. If desperate, press Solution to uncover a solving sequence. This feature is not available for the larger groups.
• In the custom mode, you're asked to define your own buttons as permutations on \(1,\ldots,9\), arranged like a keypad. Enter any arrangement of these numbers without spaces or commas.

The game is named after Frank Nelson Cole, who classified all 34 transitive permutation groups of degree 9 in 1893. It was written in HTML/CSS/JS by Benjamin Sambale. The solutions are computed with GAP, the mathematics is rendered with Katex, and the images were created with TikZ.