My Friend Evan Barr coded up a puzzle he had read about in a Mensa magazine. I suggest you click around on it a bit before reading on.

Techniques to Solve

Here is how I went about solving it, not just for one incarnation, but for any.

If we number the Grid like a Sudoku puzzle, we have box (1,1) through (4,4).

Swapping the corners

Start by setting all four corners to black by clicking them directly. This will Mess up other dots, but we will fix them later.

Swapping interior dots

There are a series of click patterns that have desired results . The first of these is for switching the state of any of the four interior dots.

If you click each of the four dots connected to a corner in either a clockwise or a counterclockwise fashion, you can swap the state of the dot in center diagonally connected.

Stated another way, clicks [(1,1),(1,2),(2,2),(2,1)] will switch (3,3). Every other dot on the board remains in the initial state.

Swapping internal side blocks.

Once you know the interior technique, you do not need to worry about maintaining the state of the interior blocks. Thus, you can use a more destructive technique to swap any of the edge blocks not in a corner. For example, to swap block (1,3), you can click on (1,2) and then block (1,1). This Will also swap block (2,3) but you can reverse that with the interior dots technique.

Chaining techniques

Once you have these set of techniques, you can chain them to solve the whole puzzle.

• Swap the corner blocks so they are all the same.
• Swapping just the edge internal blocks to get the external and internal dots in opposition.
• Follow by using Swapping interior dots to set all of the interior dots to the same color.

Additional Techniques

You won’t need these techniques but they are neat.

Swap The whole grid

It should be trivial to see that clicking in any of the corners will swap all of the blocks in the four blocks connected to the corner. Clicking all four corner blocks swaps the entire state of the grid.

Swapping just the corner blocks.

To swap the states of just the four corner blocks, click the four internal blocks one at a time in either a clockwise or counterclockwise patterns. [(2,2), (2,3), (3,3), (2,2)]

Swapping just the edge internal blocks.

To swap the blocks on the edges that are not corner blocks, click each of them in sequence in either a clockwise or counterclockwise pattern. e.g. [(1,2),(1,3),(2,3),(3,4),(4,3),(4,2),(3,1),(2,)]