Every run in a nonogram has a leftmost possible home and a rightmost one. Slide it to each in your head, and any cell covered in both positions is certain — fillable before a single crossing line has said a word. That is the overlap technique. It asks for two placements and one comparison, nothing more, and it is the tool that opens almost every grid.
What is the overlap technique?
A way to find guaranteed cells in one line, alone. Pack the run as far toward one end as the clue allows, then as far toward the other; the cells filled in both extremes must be filled in every legal placement between them. Count them once, mark them, move on — no guessing, no crossings, no waiting.
Take a row of ten cells whose only clue is 8. Packed left, the run covers cells 1 through 8. Packed right, it covers 3 through 10. The two placements disagree about the ends and agree about the middle: cells 3 through 8 are filled either way — six certain cells in a line you have not otherwise touched. Wikipedia’s technique page calls this simple boxes and teaches it on this very row; solvers mostly say overlap, because that is what the two placements do.
The count has a shortcut. A single run of length L in a line of width W keeps 2 × L − W cells: twice 8 minus 10 is 6. And there is a version with no arithmetic at all, suited to a phone screen. Count the run’s length in from the left end of the line and rest on the cell where you stop; count the same length in from the right end; everything between your two stopping cells, inclusive, is guaranteed. Eight in from the left of a ten-wide row stops on cell 8, eight in from the right stops on cell 3, and cells 3 through 8 are the same six the placements gave. If the left-hand stop comes before the right-hand one, the run is too small for its line, and there is no overlap to take yet.
A worked example, clue by clue
Multi-clue lines are where most explanations stop short, so take one all the way through: a row of 15 cells with clues 2, 6, 3.
- Find the span. Run lengths plus one mandatory gap between each pair: 2 + 1 + 6 + 1 + 3 = 13.
- Find the wiggle room. Width minus span: 15 − 13 = 2. Every run in this line keeps its length minus 2: the 2-run keeps nothing, the 6-run keeps four cells, the 3-run keeps one.
- Place the 6-run’s four. Its leftmost home: pack the 2-run hard left — cells 1 and 2, gap at 3 — so the 6 covers cells 4 through 9. Its rightmost home: pack the 3-run hard right — cells 13 through 15, gap at 12 — so the 6 covers 6 through 11. Both homes agree on cells 6 through 9. Fill them.
- Place the 3-run’s one. Leftmost, behind the packed 2 and 6: cells 11 through 13. Rightmost: 13 through 15. The agreement is cell 13. Fill it.
- Let the 2-run keep nothing. Leftmost, cells 1 and 2; rightmost, cells 3 and 4. No shared cell — a run of 2 against wiggle room 2. Nothing is wasted; the line has just shown you exactly where its freedom lives.
Five certain cells from a line with no marks on it, four of them from a clue buried in the middle. The rule for middle runs is the whole trick: everything before the run packs toward the start, everything after it packs toward the end, and the run’s two extreme homes do the rest.
When do you use it?
Immediately, and then again whenever a line’s window shrinks. Overlap is the rare technique that needs nothing from the rest of the grid — a blank line is enough — which is why it belongs at the start: it is the third move of the standard opening, right after the empty, full, and forced lines are harvested.
The trigger is one comparison: any run longer than its line’s wiggle room pays. Scan the clues for fat runs against modest widths — a 12 in a twenty-wide row, an 8 in a twelve — and take their middles first. Lines whose runs all sit at or under the wiggle room owe you nothing yet; pass them by without regret.
Then keep the tool out as the grid fills in. Overlap works on any window, not just a whole line: once X’s fence a run into a shorter stretch, run the same two placements inside the fence. A 12-wide row with a single clue of 5 gives nothing at first — wiggle room 7. Let one X arrive at cell 3 from a column you solved, and the 5 no longer fits in the two cells before it; its window is now cells 4 through 12, nine wide, wiggle room 4, and cell 8 is suddenly certain. Lines that gave nothing at the start give cells all game long, if you keep asking.
Where does it go wrong?
Three miscounts account for nearly every overlap that turns out wrong or never turns up, and each has a tell you can catch in the moment.
Wiggle room read as the prize. The subtraction gives the line’s freedom, not your cells. Clues 4, 3 on a twelve-wide row: span 8, wiggle room 4 — and since neither run is longer than 4, the overlap is zero. Marking “the four overlap cells” there plants wrong cells in an innocent line. The guarantee is run minus wiggle room, per run, and only when that is positive. The tell: you seem to be finding cells on lines whose clues are all small.
The middle of the line instead of the middle of the run’s window. Overlap cells sit between a run’s own two extreme homes, not around the row’s center. Clues 1, 7 on twelve cells: wiggle room 3, so the 7 keeps four cells — 6 through 9, pushed rightward the way the leading 1 pushes its whole window. Eyeballing “the middle of the row” and marking 5 through 8 feels the same and is wrong by one cell. The tell: you cannot write down two extreme placements that both cover the cell you just marked.
Treating it as a one-shot move. The opening pass takes the whole-line overlaps, and then the technique quietly retires — that is the waste. Every X that lands re-fences some run into a smaller window, and smaller windows mean bigger overlaps. The twelve-wide clue-5 row above is the shape of it: nothing on the blank line, one certain cell after one X. The tell is a solve that stalls while half your lines carry fresh X’s nobody has re-read.
Overlap is the nonogram’s honest opening offer: two placements, one comparison, and only what both agree on. It will not finish a grid — the line-by-line discipline does that, direction by direction — but it starts nearly every one, and it comes back whenever the grid tightens. Slide the run left, slide it right, keep the agreement. The rest of the puzzle is more of the same, smaller.
Questions
What if the overlap comes out to zero cells?
Then the line has nothing to give yet — its runs are no longer than its wiggle room. Leave it and let the crossing lines shrink some run's window; a line that offers nothing on an empty grid often pays once a few X's fence its runs in.
Can the overlap technique prove a cell empty?
No. Comparing extreme placements only shows cells that every placement fills; it never shows a cell that no placement touches. Empty cells come from other reasoning — a satisfied clue, or a stretch too short for any remaining run.
How do you find the overlap for a clue in the middle of a line?
Pack every clue before it as far toward the start as the rules allow, and every clue after it as far toward the end. The two extreme homes this leaves the middle run share exactly its length minus the line's wiggle room, whenever that is positive.
Is the overlap technique the same as simple boxes?
Yes — simple boxes is the reference-page name for the same move: cells that every legal placement of a run covers. Overlap is the solver's word for it, and the counting is identical.