Mercury: a box one clue-length in crosses out the edge

The picture

Say the first clue is 4 and there is a box on square 5, four squares in from the edge. That box has to belong to the first run, because a second run could not start before square 6. A run of 4 that includes square 5 can begin on square 2 at the earliest. If it began on square 1 it would end on square 4 and miss the box, which would then sit hard against the run and make it five long.

So square 1 is never used and can be crossed out. That is the whole technique. It settles a single square, which is why people miss it.

More than one square

If the box is really a short run of two or three, the run must cover all of it, which pushes the run further from the border. Each extra box in the run moves the earliest start one square to the right, and one more square at the edge becomes empty.

Check this on every row and column once the first boxes are in. It is quick, and the crosses it makes are at the edge, where they trigger glue and punctuating in the crossing lines.

The move in three steps

1. Find the nearest box. Look at the first box from the left or top edge.
2. Compare with the first clue. Is the box exactly one clue-length from the edge, or a run that reaches that far?
3. Cross out the end. Cross out the end square, and one more for each extra box in that run.

Worked example: one box, then two

In a row of ten with the clue 3 3 and a single box on square 4, the first run of three cannot start on square 1. It would end on square 3, directly beside the box, and the two would fuse into a run of four. So square 1 is empty.

Make it a pair of boxes on squares 4 and 5. The run of three must cover both, so it starts on square 3 at the earliest, and squares 1 and 2 are both empty.

Common slip. Applying it with a later box. The box must be the first one in the line, or the first run may not be the one that owns it.