Nonogram cheat sheet: 12 techniques
Rules of thumb in our own words. Names follow Wikipedia where it has one. Full lessons with puzzles: brainiacplay.com/nonogram/how-to-solve
1. Completing a line
Add the clue. Boxes found equal the total: cross out the rest. Open squares plus boxes equal the total: fill them all.
2. Simple boxes
Push each run to the left, then the right. Squares covered both times by the same run are boxes.
3. Counting the slack
Slack = length - (clue + gaps). A run longer than the slack fills (run - slack) squares. Redo it on what is still open.
4. Punctuating
A run as long as the biggest clue, or a finished run at an edge, cannot grow. Cross out both sides.
5. Simple spaces
If only one clue is left, it can only reach so far from the boxes it must cover. Cross out beyond it.
6. Glue
A box nearer to a wall than the first (last) clue is long pins that run. Fill from the box to where the run reaches.
7. Mercury
A box exactly one clue-length from a wall: that run cannot start earlier, so the wall square is empty.
8. Forcing
Crosses split a line into rooms. Clues keep their order, so place them in the rooms that fit. Narrow rooms are empty.
9. Joining and splitting
One open square between two boxes: join if a split leaves the run too short, split if a join makes it too long.
10. Cross-referencing
Settle one line, then the lines crossing the squares you changed. Repeat: row, column, row, column.
11. Contradictions
Out of moves? Pencil a square. If a line then has no legal layout, the opposite is certain. If nothing breaks, rub it out.
12. Deeper search
Chain one proof after another, finishing each. A try inside a try is the last resort, mostly for computers.
Always work in this order: complete lines, simple boxes, punctuate, then the edge and room rules, then switch direction. Never guess. Brainiac Play