Tier 2
Locked queen placement
Squares attacked by every remaining option are dead — even before you know which option is right.
You do not need to know where a queen goes to know what she will kill.
Take a region with three surviving squares. Each of them attacks its own eight neighbours. Look at the overlap: any square touched by all three is doomed, because wherever this region’s queen ends up, that square is next to her.
This is the first technique that produces certainty out of pure uncertainty, and it is the one that makes people fall for the game.
Where the overlap actually happens
Only when the candidates are clustered. Three squares scattered across a big region share no neighbours and the technique finds nothing. Two adjacent squares in a corner share five. So scan for tight regions — two or three surviving squares packed together — and check the ring around them.
The same reasoning works for rows and columns, not just colours. If a row’s last two options are (4, 5) and (4, 6), then (3, 5), (3, 6), (5, 5) and (5, 6) are all attacked either way, plus the diagonals. That is four to six free eliminations from a row you had written off.
Related
The rule of clumps is the sharpened version of this idea applied to two neighbouring lines at once, and it is where genuinely hard boards start.