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Puzzle Quarry

Hitori 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 measures it.

Ordered by how much you have to hold in your head

The ladder is an order to try things in rather than a list of tricks to memorise, and on this puzzle the order comes out unusually clean. Each rung asks you to take in a wider piece of the board than the one below it: two or three printed numbers, then one decided cell and what touches it, then a corner, then a pocket, then the shape of the whole surviving region. Nothing about that ordering is a matter of taste — it is how much of the grid you have to be looking at.

Each rung is also made cheaper by the rungs beneath it having been exhausted. Tracing a region while half the board is still undecided means tracing something that is about to change; the same trace after one more sweep of consequences is over a shape that has settled down. Players who describe hitori as tedious are nearly always doing the expensive thing while a free one is still available.

What is striking is how few of these there are. Three of the five rungs are the same rule at three sizes, and that is not padding: the connectedness rule is what this puzzle is about, and the only thing that varies is whether the piece it would seal off is a corner you recognise, a pocket you count, or half the board.

How a board earns the level it ships with

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 cell is decided, and it records the highest rung it ever stood on. Easy stops at the cascades. Medium reaches the corner. Hard reaches the pocket. Expert reaches the division of the board.

Nothing is graded by how many numbers repeat and nothing is relabelled afterwards. A board cannot be capped while it is being grown the way a grid can be while it is being carved, so boards routinely come out at a level other than the one requested, and the answer to that is to ship the level measured rather than the level asked for.

There is a sixth rung and nothing here is allowed to stand on it. Painting a cell, following it until something breaks and scrubbing it out again will finish any board whatsoever, which is exactly why it cannot be part of a difficulty scale. Its page explains how to do it properly if you meet one elsewhere, and why the generator throws away everything that needs it.

The rung that was measured and left out

A sixth argument was written for this engine and does not appear on the ladder. It is the one binary puzzle solvers know as line analysis: list every legal way a single row could be painted, then keep whatever all of those ways agree on. It is sound, it is a real technique that real people use, and on this puzzle it is very nearly useless.

The reason is that the connectedness rule gets there first almost every time. Run both across thousands of generated boards and line analysis turns out to be the hardest argument required on about one board in a hundred; every other board that needs it also needs a cut, and the cut is what the difficulty ends up being measured as. A rung that fires on one board in a hundred is not a difficulty level, it is a rounding error with a name.

So it was taken out rather than kept for the look of the thing. A ladder is a claim about what boards require, and a rung nothing requires makes every label on the site slightly less true.

Common questions

How many techniques does a hitori board need?

Five, and most boards need three of them. The printed patterns and the cascades that follow will finish an easy board on its own; the three sizes of the connectedness argument are what each further level of difficulty means here.

Which hitori technique should I learn next?

Whichever one your current level stops at. Stalling on medium means the corner argument is not yet a habit; stalling on expert means tracing the region is not. The hint names the argument it used, which is the fastest way to find your own gap.

More Hitori pages