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Puzzle Quarry

Skyscrapers Solving Techniques

Six 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 measures it.

Ordered by what the move costs your attention

The ladder is an order to try things in rather than a set of tricks to collect, and its order is not the one a machine would choose. Listing the ways a street of five could be arranged is trivial for a computer and takes a person a pencil and a margin; sweeping a column for a height with one lot left is the reverse. This ladder is a model of attention, not of processor time, which is why the written-out street sits near the top.

Each rung is also made cheaper by the rungs beneath it having been exhausted first. A street considered while all its lots are wide open may have sixty orderings; the same street after two heights have gone in may have three. Anybody who describes this puzzle as an exercise in enumeration is almost certainly doing the expensive rung while a free one was still available.

That ordering is also what makes the difficulty labels mean anything. A solver that always takes the cheapest move it can find, and is then cornered into an expensive one, has established something real about the board — nothing simpler was available at that moment. A solver that reached for the expensive move first would have proved only that it was written badly.

Where the four labels come from

Every published board goes through the same solver the hint button uses. It applies the cheapest argument that fits, over and over, until every lot holds one height, and it records the highest rung it ever stood on. Easy stops at the sweeping. Medium reaches the height that has to be tried and rejected. Hard reaches the written-out street. Expert reaches the argument that holds the numbers at both ends of a street in mind together.

Nothing is graded by how many numbers are printed and nothing is relabelled afterwards. The generator rubs out one number at a time and stops the moment the next removal would need an argument above the level’s cap — so a board can come out easier than the level asked for and can never come out harder. When it comes out easier it ships under the level it measured, which is the only labelling this site does.

There is a seventh rung and nothing here is allowed to stand on it. Trial — write a height, 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 every board that needs it is discarded during generation.

Common questions

How many techniques does a skyscrapers puzzle need?

Six, and most boards need three or four. Reading the rim and crossing out finish a gentle board between them; the rest are what each further level of difficulty means here.

Which skyscrapers technique should I learn next?

Whichever one your current level stops at. Stalling on medium means you are not yet testing a height against a view; stalling on expert means you are reading each end of a street separately.

More Skyscrapers pages