Nonograms: the overlap rule
Slide a block as far left as it goes, then as far right. The cells it covers both times are filled, wherever it really sits.
How it works
A clue tells you a block’s length, not its place. But a long block can’t move far. Some cells are covered wherever it goes.
Push the block as far left as it will go. Then as far right. Every other placement sits between these two, so a cell covered by both is covered by all of them. Fill it.
This is the overlap rule. It needs nothing but the clue and the line length, so it is the first thing to try on an empty puzzle.
The slack shortcut
The slack is the line length minus what the clue needs. A 7 in a row of 10 needs 7 cells, so the slack is 3.
Each block fills its length minus the slack, counted in from its leftmost place. A 7 with slack 3 fills 4 cells. A block no longer than the slack fills nothing.
More than one block
With several blocks, the gaps count. “3 4” needs 3 + 1 + 4 = 8 cells, so in a row of 10 the slack is 2. Compare each block with itself: the 3 always covers cell 3, and the 4 always covers cells 7 and 8.
Worth memorizing
Push left, push right, fill what both cover.
Slack = length − blocks − gaps.
Each block fills its length minus the slack.
Compare a block with itself.
Where the 3 sits and where the 4 sits never mix.
Practice
0 of 5 rightHow many cells does the overlap rule fill here?
How many cells does the overlap rule fill here?
How many cells does the overlap rule fill here?
Which cells does the overlap fill?
Which cells are sure to be filled?