The Arrow Board Analyzer runs machine verification algorithms to guarantee that every board configuration has zero circular deadlock traps and at least one valid sequence of moves leading to a full board clear.
Interactive Arrow Board Analyzer & Solvability Inspector
Whether testing hand-built custom puzzles or inspecting preset challenge levels, our machine solver checks directed path collisions, calculates free exit ratios, and identifies critical bottleneck arrows holding up board progression.
How the Board Solvability & Bottleneck Algorithm Works
1. Path Ray Casting
Every arrow's direction is cast along a straight line vector from its arrowhead cell to the outer edge of the grid. If no non-removed arrow cells lie on this vector, the arrow is flagged as an active exit.
2. Dependency Graph Mapping
When an arrow is blocked by other arrows, the analyzer creates a directed dependency graph. Arrow A depends on Arrow B if B occupies a cell along A's exit lane.
3. Deadlock Detection
A circular dependency (e.g. A blocks B, B blocks C, C blocks A) creates an unsolvable deadlock. The analyzer checks for cycles in the dependency graph to guarantee 100% solvability.
Identifying Dependency Deadlocks & Critical Chains
In high-density boards like Level 1 Rooster (155 arrows) or Level 2 Elephant (165 arrows), clearing perimeter arrows is easy, but unlocking the core requires finding the Critical Bottleneck Arrow. Removing this specific arrow unlocks the highest number of downstream exit lanes, starting a domino effect of consecutive free moves.
Frequently Asked Questions
How does the Arrow Board Analyzer verify solvability?
The analyzer executes a topological graph traversal on the directed grid, simulating every playable arrow exit to verify if a complete 100% clearing path exists without entering deadlock cycles.
What is a Critical Bottleneck Arrow?
A Critical Bottleneck Arrow is a key arrow blocking the highest number of downstream arrows. Removing it unlocks the maximum number of newly free exit lanes on subsequent turns.