When a colour owns a line

The forward direction: a colour claims a line

Suppose the mint region has four open squares left and all four of them sit in row 6. You do not know which one takes mint's queen, and you do not need to. What you know is that mint's queen is in row 6 — and since a row holds exactly one queen, no other colour may use row 6 at all. Every square in that row belonging to a different colour can be crossed out on the spot.

On a wide board this is a large move. A 12x12 row that mint occupies four squares of leaves eight squares belonging to other colours, all of them dead at once. Those eight eliminations frequently collapse two or three other colours down toward a single open square, which is why a lock is so often followed immediately by a run of forced placements.

The same argument works for columns without modification. If every open square of a colour lies in column 3, column 3 is that colour's and everyone else is out.

Spotting it before it is obvious

The easy case is a region that is physically shaped like a bar: a colour drawn as five squares in a straight horizontal line is locked to its row from the very first move, before you place anything at all. Boards that contain one of these are noticeably easier, because you get a free elimination sweep for nothing. It is always worth scanning for them before your opening move.

The harder and more valuable case is a region that becomes locked partway through. A colour spread over three rows loses its squares in two of them as queens go down elsewhere, and suddenly everything it has left is in one row. Nothing about the drawing of the board changed; the lock appeared because of what you eliminated. This is why the technique is worth re-checking after every few placements rather than only at the start.

A practical trigger: whenever you cross out squares in a row, glance at which colours just lost ground there and check whether any of them is now confined to a single line. The information is right in front of you at the moment you make the elimination and much harder to find ten moves later.

The reverse direction: a line claims a colour

Now run the argument the other way. Suppose every open square remaining in column 9 belongs to the khaki region — no other colour has a survivor in that column. Column 9 must contain a queen, and only khaki can supply it, so khaki's queen is in column 9. Every khaki square anywhere else on the board is now dead.

This is the same logical shape as the forward case, but the eliminations land in a completely different place. In the forward case you cross out squares on the line; in the reverse case you cross out squares off the line, in whatever far corner of the board the colour happens to reach. Players who know only the forward direction routinely miss these, because nothing in the line itself looks interesting — the signal is that other colours are absent.

Both directions are the two-element case of a more general pattern. When two colours between them occupy exactly two lines, or three colours exactly three lines, the same exclusion applies to the whole group. That generalisation is the pairing argument, and it is the subject of its own article.

What it is not

A lock is not a placement. It tells you which line a queen is on, not which square. Trying to guess the square is exactly the kind of move that ruins a single-solution board — you will be right about half the time and spend longer unwinding the other half than the whole puzzle deserved.

It is also not permanent in the sense of needing no follow-up. Once you have established the lock and made its eliminations, re-run both sweeps immediately. The eliminations are the point; the lock itself does nothing for you until you spend it.