When to write candidates — and how much

The short version

Candidates are information, and information has a cost. On a board that is still resolving by eye, a full candidate grid makes you slower: eighty-one cells of small digits compete with the numbers you are actually looking at.

The rule that works: mark when scanning stalls, not before. And when you do mark, mark less than you think you need.

The cost, stated honestly

A full candidate grid is up to 729 small digits. In practice a mid-game board has around 50 empty cells at three or four candidates each, so 150 to 200 marks — which is a lot of pencil work, and a lot of ink on a small surface.

The cost is not the writing. It is the reading. Every technique in the middle game requires you to compare candidate lists across cells, and the more marks there are, the more the useful ones hide among the useless ones.

This is why strong solvers mark less, not more. They are not being lazy; they are keeping the signal-to-noise ratio high.

When the grid earns its cost

There is a clean trigger, and it sits at a specific boundary in the technique ladder.

• Before the boundary — singles, pointing, claiming — every move can be found by counting visible digits in a unit. Candidates add nothing.
• After the boundary — pairs, triples, fish, wings — every move requires comparing candidate lists. Candidates are mandatory.

The boundary is: the point where a complete sweep of pointing and claiming returns nothing. That is the moment the board has stopped being readable at a glance.

A secondary trigger, for puzzles you are learning on: mark as soon as you feel the urge to guess. The urge usually means the board is no longer legible, which is the same signal.

Mark less: three ways

Mark only congested units

If one box has five cells at three candidates and the rest of the board is resolving normally, mark that box. The other eight are noise until they stop resolving.

Mark only nearly-finished digits

A digit with three homes left is interesting. A digit with six is not. Mark the 3s or the 7s if they are close to completion, and leave the wide-open digits blank — you can count their homes by eye.

Mark only what a specific technique needs

If you are hunting an X-Wing on 4, you only need the 4s. Writing a full grid to find a technique that reads one digit is wasted work. This is the single biggest efficiency gain available to an intermediate solver.

Keeping it legible

Whatever you mark, mark it the same way every time.

Use a fixed nine-position layout inside each cell — reading order, always:

`` 1 2 3 4 5 6 7 8 9 ``

A 7 is always bottom-left. After a few puzzles you read positions instead of digits, which is faster and far less error-prone. A missing digit becomes a hole you can spot at a glance rather than something you have to check by reciting.

Cell and box notation, if any of the names above are unclear.

When to erase

Candidates should be removed when a digit is placed, not when someone reminds you.

The mechanical discipline: after every placement, delete that digit from the candidate lists of all cells in the same row, column and box. This is the only maintenance step, it takes ten seconds, and skipping it is the single most common source of "stuck" boards.

If you are solving on paper, erase as you go. If you are solving in an app, most of them maintain this automatically — which is convenient, and also why solvers who learn in apps often have weaker candidate hygiene when they move to paper.

The trap: marking as avoidance

There is a failure mode that looks like diligence. The board stalls, so you fill in every candidate in every cell, neatly, in fixed positions. Twenty minutes pass. The board is now beautiful and still unsolved.

Marking is not solving. If you have marked everything and the board is still stuck, the next move is not to mark more carefully — it is to run a sweep at the next technique level, or to re-verify a completed unit.

Where to use it

Marking strategy is a personal matter, and any consistent approach beats an inconsistent one. But the direction of improvement is clear: solvers who get faster almost always do it by marking less and scanning more systematically, not by marking more thoroughly.

If you are unsure where to start, try this for ten puzzles: no candidates at all until the board stalls, then mark only the digit you are actively hunting. Most people find they finish faster, and that the full grid was never necessary.