Master the advanced technique for solving hard puzzles.
Elimination is a logical deduction technique used in Akari (also known as Light Up) puzzles when basic rules alone cannot make progress. Instead of proving where a light bulb must go, you prove where it cannot go by assuming the opposite and watching for a contradiction.
In a typical Akari puzzle, you start by applying straightforward rules: a numbered wall cell with all its neighbors accounted for, or a cell that can only be reached by one remaining position. These basic deductions carry you through easy and medium puzzles. But when you face a hard puzzle — especially the 12×12 grids on GridPaw — you will hit a wall where no obvious move presents itself. That is exactly where the elimination technique earns its place in your toolkit.
The core idea is simple: assume a cell is a light bulb, then check whether that assumption leads to an impossible state. If it does, the cell must be empty. If assuming a cell is empty leads to a contradiction, then it must be a light bulb. Either way, you gain information without guessing.
Before you can use elimination effectively, you need to know what a contradiction looks like in an Akari puzzle. There are four common contradiction types:
Training your eye to recognize these four patterns is the key to making elimination fast and reliable. With practice, you will start seeing contradictions within seconds of placing a hypothetical bulb.
Let us walk through a concrete example to see elimination in action. Imagine you have a section of an Akari grid where two empty cells — call them A and B — sit in a corridor between several numbered walls. Basic rules have stalled, and you need to decide: is cell A a light bulb, or is it empty?
Pick a cell that, once resolved, would unlock several other deductions. Good candidates are cells that sit at intersections of multiple constraints — near numbered walls, in narrow corridors, or at the only position that can illuminate a specific dark cell.
Place a hypothetical light bulb in cell A. Now propagate all consequences: mark every cell this bulb illuminates along its row and column until walls block the beams. Check adjacent numbered wall cells — do any exceed their allowed bulb count?
Scan for the four contradiction types. Does any wall number get violated? Does any remaining empty cell become permanently unreachable? Do two hypothetical bulbs shine directly on each other? If you find a contradiction, you have proven that cell A cannot be a light bulb — mark it as empty.
If assuming A is a bulb produces no contradiction, try assuming A is empty instead. Sometimes the contradiction appears on the other side. If assuming A is empty also produces no contradiction, this particular elimination test is inconclusive — pick a different candidate cell and come back later.
Once elimination gives you a definite answer (bulb or empty), mark it and immediately re-check all nearby constraints. A single resolved cell often triggers a chain of basic deductions that were previously blocked. Then pick your next candidate and repeat the process.
You might wonder: how do I know when to switch from basic rules to elimination? Here are the signals:
The transition from basic solving to elimination is not a failure — it is a sign that you are tackling genuinely challenging Akari puzzles. The best solvers use elimination as a natural extension of their basic toolkit, not as a last resort.
Elimination can be slow if you test every cell blindly. Use these strategies to speed up:
The best way to internalize elimination is to practice on real Akari puzzles. Start with medium-difficulty puzzles where basic rules get you 70–80% of the way, then use elimination to finish. As your recognition of contradiction patterns improves, move up to the hard 12×12 puzzles that require elimination from the start.
GridPaw offers puzzles at every difficulty level, all playable directly in your browser. The hard puzzles are specifically designed to require elimination — they are excellent training grounds for this technique.
No. Guessing means placing a light bulb and hoping it works. Elimination means placing a hypothetical bulb, checking for a logical contradiction, and drawing a definite conclusion. The difference is that elimination always produces a provable result — either the assumption leads to a contradiction (proving the cell is empty) or it does not (which you then test from the other direction). You never have to backtrack from a guess because you never commit to an unproven placement.
It varies. In a well-designed hard Akari puzzle, you typically need elimination two to five times. Each elimination resolves one or two cells, which then unlocks a cascade of basic deductions. The hardest puzzles may require elimination at nearly every step, but those are rare even among 12×12 grids.
Technically yes — elimination subsumes basic rules since a "forced move" is just an elimination where the contradiction appears immediately. However, solving exclusively through elimination is much slower. The most efficient approach is to apply basic rules first for speed, then switch to elimination only when you get stuck. This hybrid strategy is what experienced Akari players use in competitive or timed solving.
