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Puzzle Quarry

Bridges Solving Techniques

Five arguments, in the order to reach for them. The hardest one a board forces on you is that board’s difficulty — on this site, and in the code that grades it.

Ordered by what it costs a person, not a computer

The ladder is an order to try things in rather than a list of tricks to memorise, and its order is deliberately not the order a machine would choose. Striking a link out because a bridge already crosses it is almost free for a person — the bridge is right there, you can see it — and it sits below the arithmetic even though a computer finds the arithmetic easier. The ladder is a model of attention, not of processor time.

Each rung is also made cheaper by the rungs below having been exhausted first. Weighing an island whose links are all still wide open means considering everything; the same island after one more sweep may have two of its links already closed and answer itself. Players who describe bridges as tedious are almost always doing the expensive move while a free one is still available.

The order pays off in the grading too. Because the solver always takes the cheapest available move, the hardest move it was ever forced into is a genuine statement about the board: it means nothing simpler existed at that moment, not merely that the solver failed to notice something.

How a board gets its label

Every published board is run through the same solver the hint button uses. It applies the cheapest argument that fits, over and over, until every link is decided, and it records the highest rung it ever stood on. Easy stops at island counting. Medium reaches the crossing rule. Hard reaches the capacity arithmetic. Expert reaches the connectivity argument.

Nothing is graded by island count and nothing is relabelled afterwards. Because a network cannot be capped while it is being grown the way a grid can be while it is being carved, boards routinely come out at a level other than the one requested — and the answer to that is to ship the level measured, not the level asked for. Ask for expert on a 7×7 and you may well get a hard board, because seven columns sometimes do not leave a group enough room to seal itself off.

There is a sixth rung and nothing here is allowed to stand on it. The assumption — draw a bridge, follow it until something breaks, rub it out — will finish any board whatsoever, which is exactly why it cannot be part of a difficulty scale. Its page explains what it is, and why the generator throws away every board that needs it.

Common questions

How many techniques does a bridges puzzle need?

Five, and most boards need three of them. Island counting finishes an easy board on its own; the crossing rule, the capacity arithmetic and the connectivity argument are each what one further level of difficulty means here.

Which bridges technique should I learn next?

Whichever one your current level stops at. Stalling on medium means the crossing rule is not yet a tool you use; stalling on expert means the connectivity argument is. The hint names the argument it used, which is the quickest way to find your own gap.

More Bridges pages