How to Solve a Five-Move Puzzle

Start by surveying the puzzle

This puzzle has more color than the one in the first walk-through. In particular, cell 22 is lime. The color wheel tells us that lime is three steps away from black.

We can use inspection in reverse

Neighbor relationships work both ways. If a cell is a neighbor of 22, then 22 is also one of that cell’s neighbors. Inspecting cell 22 therefore shows the six cells we might click to change it.

Because cell 22 is three steps from black, exactly three of those neighbors must be clicked during the solution. We’ll come back to this cell later.

Look for a constrained cell

Now look at cell 2. It is plum, so it needs to advance only once to reach black. That means exactly one of its neighbors should be clicked.

Inspection shows the four possibilities: cells 1, 3, 5, and 6.

Rule out moves that create tangerine

Suppose we clicked cell 3. That would clear cell 2, but it would also change the black cells 6 and 7 to tangerine.

A tangerine cell is four steps from black. Since the entire puzzle is supposed to take only five moves, creating tangerine is undoubtedly a mistake.

Eliminate the other bad choices

Clicking cell 6 has the same problem: it would change black cells 3 and 7 to tangerine. We can rule that out too.

Choose the promising move

That leaves cell 1 as the only promising way to clear cell 2. Inspection confirms that clicking 1 will also clear 6, without any obvious bad side effects.

Make the first move

Click cell 1. Cells 2 and 6 become black, and the puzzle is already starting to look simpler.

Recognize a half-donut

Using the same reasoning, we could determine that clicking cell 8 is the promising way to clear cell 4. But there’s also a visual clue.

Cells 4, 9, 13, and 14 form a kind of half-donut: four plum cells curving around the black center at 8. The shape suggests that a click in the donut hole might clear the entire group. Inspection confirms it.

Clear the half-donut

Click cell 8. The four surrounding plum cells all advance to black.

Find the next donut

Now another donut appears, this time with its hole at cell 16. Its ring is not entirely plum, but inspection shows that clicking the center still has no apparent bad side effects.

The endgame takes shape

Click cell 16. We now need only two more moves, and almost every colored cell is plum.

Finish from the edge

We can apply the same logic we used for cell 2 to cell 25. The only promising way to clear it is to click 26.

After that move, the only colored cells are the three plum cells in the corner. One final click on 27 clears all three and solves the puzzle.