The order in which to look for things

The short version

Every technique has a price, and the price is attention. Singles cost a glance. Fish cost a minute of counting. Chains cost whatever is left of your patience.

A stalled board is almost always a board where a cheap move was missed while an expensive one was being hunted. So scan in a fixed order — cheapest first — and only escalate when the current level produces nothing at all.

The order

This is the order that works, and it is stable across difficulty levels:

1. Naked singles — cells with one candidate left.
2. Hidden singles — digits with one home left in a unit.
3. Box-line reduction — pointing and claiming, both directions.
4. Naked pairs and triples — identical short candidate lists in one unit.
5. Hidden pairs and triples — digits confined to the same small set of cells.
6. Fish — X-Wing, Swordfish, Jellyfish.
7. Wings — XY-Wing, XYZ-Wing, Skyscraper.
8. Uniqueness and chains — unique rectangles, forcing.

The ordering is not arbitrary. Steps 1 and 2 need no candidate grid. Step 3 needs a single count per box or line. Steps 4 and 5 need the grid. Steps 6 and 7 need the grid and a systematic count across parallel lines. Step 8 needs all of it plus bookkeeping.

One sweep, defined precisely

"Scan for singles" is not an instruction until you say what a complete sweep means. Here is a definition you can actually finish:

• For every digit 1 through 9:
• check every box for that digit;
• check every row for that digit;
• check every column for that digit.

That is 9 × 27 = 243 questions, and most of them are answered in under a second once you are practised. If any of them produces a placement, make the placement and restart the sweep from digit 1. Do not continue from where you were — the board has changed underneath you.

A sweep that returns nothing across all 243 questions is a real signal. That is when you escalate.

Why escalating too early is the common failure

The failure mode is not laziness. It is boredom.

Singles are repetitive, and after a few empty passes the temptation is to go looking for something interesting — an X-Wing, a wing, a chain — because those feel like progress. Meanwhile the actual blocker is a hidden single in a box you have already swept twice, which appeared the moment you made your last placement and which no one has looked for since.

The discipline is: escalate only after a complete empty sweep at the current level. Not after two boxes felt stuck. Not after the board "seems" hard. A full sweep, then move on.

When to write candidates

Timing matters as much as order. The grid should appear at the boundary between step 3 and step 4.

Before that boundary, candidates are overhead: steps 1 to 3 can all be done by counting visible digits. After it, candidates are mandatory: you cannot compare two candidate lists without having written them.

The practical trigger: when pointing and claiming across all digits produce nothing. At that point the board has stopped being readable at a glance, and the grid earns its cost. Writing it earlier makes you slower. Writing it later means you are guessing at pairs from memory, which is how false patterns happen.

More on when and how to pencil-mark.

What to do when everything comes back empty

If you have run a complete sweep at every level and the board is still stuck, suspect the board before you suspect the puzzle.

1. Re-verify one completed unit. Take the fullest row and add up its digits. A single wrong entry poisons every candidate downstream, and the symptom is exactly this: a board where nothing works.
2. Check for a second solution. If a puzzle has two solutions, some standard techniques will refuse to fire, because they quietly depend on uniqueness. That is rare in published puzzles and common in hand-made ones.
3. Look at the candidate count. If several cells have three or more candidates and none are two, you are in fish-and-wing territory and there is no cheap move to find. That is not a mistake, it is the puzzle.
4. Only then consider a chain. Forcing is legitimate, slow, and should be the last resort rather than the first.

Where to use it

Use the same order every time, including on easy puzzles. The habit is what makes hard boards tractable: when the puzzle finally stalls, you know exactly which sweep you have already run empty, so you are never guessing about where to look next.

There is a second benefit that is easy to miss. A fixed order makes your mistakes findable. If a board is stuck and you know you ran a full sweep at every level, the problem is almost certainly a bad candidate rather than a missed technique — and that is a much smaller thing to go looking for.