What do I do when the easy moves run out?

Stop looking for where a queen goes and start looking for where queens can't go. Two ideas do most of the work: a colour whose open tiles all sit in one row or column claims that whole line, and a row or column whose open tiles are all one colour claims that whole colour. Both let you cross out tiles, which exposes the next forced queen.

1. A colour trapped in one line

Look at each colour's open tiles. If they all lie in a single row or column, that colour's queen will be in that line, wherever it ends up. The line gets only one queen, so no other colour can use it.

queenalready ruled outplay herecross out nowtiles to look at

Every open tile of the jade colour is in row 1, so its queen must go in row 1. No other colour can use row 1: cross out the rest of it. Full page: A colour trapped in one line.

2. A line trapped in one colour

This is the same idea turned around. If every open tile in a row or column is the same colour, that line's queen will be that colour's queen. So the colour's tiles outside the line can't hold a queen.

Every open tile in row 1 belongs to the lagoon colour, so that colour's queen must be in row 1. Cross out its tiles everywhere else. Full page: A line trapped in one colour.

A routine for medium boards

1. Take every forced queen: any row, column or colour with one open tile.
2. For each colour, ask: are all its open tiles in one row or one column? If so, clear the rest of that line.
3. For each row and column, ask: are all its open tiles one colour? If so, clear that colour elsewhere.
4. Go back to step 1. Crossing out usually creates a new forced queen.

Small and thin colours are the ones that get trapped first, so check those before the big ones.

Still stuck on harder boards?

The expert guide covers pairs, triples and the no-room test.