📖 Constraint Propagation

Akari Puzzle Glossary — All Terms

Constraint Propagation — Constraint propagation is the foundational solving technique in every Akari puzzle. It works by examining numbered cells and deducing forced placements or eliminations.

⚙️ How It Works

Start by examining numbered cells. A "4" forces all four neighbors to be bulbs. A "0" eliminates all four neighbors. After each placement, propagate the consequences — newly placed bulbs illuminate rows and columns, which may trigger further deductions. Repeat until no more simple deductions are available.

⚖️ Pros & Cons

✅ Advantages

  • Solves Easy and Medium puzzles completely without advanced techniques
  • Deterministic — no guessing required
  • Fast and systematic — scan numbered cells in order

⚠️ Trade-offs

  • Hard puzzles may reach a point where simple propagation is insufficient
  • Requires careful tracking of which constraints have already been processed

🎯 Who Should Use It?

All players. Constraint propagation is the first technique to apply on every puzzle. If it solves the puzzle completely, you do not need advanced methods.

🚀 Step-by-Step Guide

1

Scan for "4" and "0"

These give the most information. Place bulbs around "4" cells, mark X around "0" cells.

2

Propagate immediately

After each placement, check if it triggers new constraints. A newly placed bulb may satisfy a numbered cell's count, allowing you to mark remaining neighbors as X.

3

Repeat until stuck

Keep scanning numbered cells and propagating. When no more simple deductions are available, move to elimination or backtracking.

❓ FAQ

What is constraint propagation in Akari?

It is the process of examining numbered cells, deducing forced placements or eliminations, and then propagating those consequences to find more deductions. It is the primary solving technique for Easy and Medium puzzles.

Can constraint propagation solve every Akari puzzle?

Easy and Medium puzzles, usually yes. Hard puzzles on larger grids may require additional techniques like elimination chains or backtracking.

Ready to put this knowledge to use?

🐱 Play GridPaw Free