Reverse Thinking: Solve Arrow Puzzles Backward

Forward planning hits a wall around level 30. That's when the dependency chains get long enough that you can't hold every possible sequence in your head. The solution? Think backward.

What Is Reverse Thinking?

Instead of asking "what should I do first?", ask "what must happen last?" The final state of any arrow puzzle is an empty board. The last move is always an arrow escaping from the edge or moving into the last empty cell. By identifying that final move and working backward, you can unravel the entire solution.

How to Apply It

  1. Find the likely final arrow. Which arrow, after everything else is gone, has a clear path to escape? Usually it's one near the center that will be unblocked after surrounding arrows are removed.
  2. Identify what blocks it. What arrows are in the way of this final arrow? These must be removed first.
  3. Repeat for each blocker. For each blocking arrow, what blocks it? Continue until you reach arrows that can move immediately (edge-facing or facing empty cells).
  4. Reverse the chain. The arrows you identified last (the freely movable ones) are your first moves. The final arrow you identified is your last move.

Example: A Simple Chain

Imagine three arrows: A is at the bottom pointing up, B is above A pointing up, and C is at the top pointing up. C can escape immediately. After C escapes, B can move upward into C's old spot, then escape. After B escapes, A can move up and escape.

Forward thinking: "I move C, then B, then A." This is easy for three arrows but nearly impossible for nine. Backward thinking: "A escapes last. A is blocked by B. B is blocked by C. C is free. So: C → B → A."

When to Use This Strategy

Reverse thinking becomes essential around the Chains stage (levels 21–80), where dependency chains of 3–5 arrows are common. It's also invaluable for the Branches stage, where multiple arrows may need to be cleared before a single blocker can move.

For very dense boards (200+), combine reverse thinking with edge-first scanning: identify the "deepest" arrow (the one most entangled in the center) as your final target, and work outward.

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