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The game board
consists of two squares, each with nine checkboxes arranged in three rows. A checkbox may be either checked or unchecked. In the left square, the checkboxes behave as one would expect of a regular checkbox - clicking on it toggles its state. In the right square the behavior is different. Namely, a click on a checkbox in the right square toggles its state and some or all of the adjacent boxes. The goal of the game is to match check patterns in two squares. Obviously, the game is trivial if played on the left square. It's far from simple if played on the right one.
On the other hand, modifying initial pattern in the left square may actually make the game more difficult. The choice is yours.
For each of the games there are just three rules for playing on the right square. For the game #1 the rules are
- A click on a corner box affects its state and that of all three of its neighbors.
- A click on a box in the middle of a side affects only three boxes on that side.
- A click on the middle box toggles the state of the five boxes that form a cross in the middle of the square.
For the second game the rules are slightly different:
- A click on a corner box affects its state and that of two of its neighbors - one in the same row, another in the same column.
- A click on a box in the middle of a side affects three boxes on that side and the middle box.
- A click on the middle box toggles the state of the five boxes that form a cross in the middle of the square.
The third game is much the same as the second one except the click on the middle box does not affect other boxes.
That's it.
A note aside. You may be curious to learn that there exists a fine though simple theory that confirms existence of the solution for any starting configuration. The theory employs 9-dimensional binary space and eventually finds the solution by solving a system of 9 linear equations. Details can be found in
Don Pelletier, Merlin's Magic Square, The American Mathematical Monthly, v94, n2, 1987, p143-150.
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