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Puzzle Quarry

Binary Puzzle Solving Techniques

Five techniques, in the order a solver should reach for them. The hardest one a grid forces you to use is that grid’s difficulty — here, and in the code.

Cheapest first, always

The ladder is not a list of tricks to know, it is an order to try things in. Each rung costs more attention than the one below it and, crucially, each one is made easier by the rungs below having been exhausted first: a line with two cells left is trivial to analyse, and it got down to two cells because pairs and counting had already been applied to it.

Reaching up the ladder early is the most common way to make a binary puzzle harder than it is. Analysing a line with six holes means considering a dozen arrangements; the same line after one more sweep for pairs may have three holes and two arrangements. Players who describe the puzzle as tedious are usually doing the expensive move first.

The order also has a practical payoff on this site. Because the solver always takes the cheapest available step, the hardest step it was ever forced into is a genuine statement about the grid — it means no simpler route existed at that moment, not merely that the solver did not notice one.

How a grid gets its label

Every published puzzle is run through the same solver a hint uses. It applies the cheapest technique that fits, over and over, until the grid is full, and it records the highest rung it ever had to stand on. Easy stops at pairs, medium reaches counting, hard reaches line analysis, expert reaches twin elimination.

Nothing is graded by clue count and nothing is relabelled after the fact. If a grid intended as expert turns out to be finishable without the third rule, it is thrown away and another is generated rather than sold as hard — which would be the easy way out and would make every label on the site mean slightly less.

There is a sixth rung, and no puzzle here is allowed on it. The assumption technique — put a symbol in, follow it until it breaks something, write the other one — will finish any grid at all, which is exactly why it cannot be part of a difficulty scale. Its page explains what it is and why the generator refuses to ship puzzles that need it.

Common questions

How many techniques does a binary puzzle need?

Five, and most grids need two or three of them. Doubles and sandwiches finish an easy puzzle outright; counting, whole-line analysis and twin elimination are each what one further level of difficulty means.

Which technique should I learn next?

Whichever one your current level stops at. If you finish medium puzzles but stall on hard, the missing idea is line analysis; if you finish hard but stall on expert, it is twin elimination. The hint button names the technique it used, which is the fastest way to find your own gap.

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