Nonograms — also called Picross, Griddlers or Hanjie — hide a picture inside a grid, and you reveal it using only the number clues along each row and column. They look cryptic at first, but they run on a handful of logical moves you can learn in one sitting. No artistic skill required; it's pure deduction.
Reading the Clues
Each row and column has a list of numbers. The numbers are the lengths of the filled runs, in order, with at least one empty cell between them. A clue of “4 2” on a row means a block of four filled cells, then a gap, then a block of two, in that order. Your task is to work out exactly where those blocks sit using the clues from the crossing direction.
Start Where the Numbers Are Biggest
The easiest entry point is any line whose clues nearly fill it. In a ten-cell row, a clue of “10” fills every cell; a clue of “8” guarantees the middle six are filled no matter how the block slides. This “overlap” technique — marking the cells that are filled in every possible position of a block — is the single most useful move in the whole puzzle, and big clues give you the most overlap.
Measure the Slack
To judge which lines to work first, measure how constrained they are. A constrained line is one where the clue numbers leave very little room to shift. The degree of constraint is easy to calculate: add up all the clue numbers for a line, add one for each gap between runs, and subtract from the line length. The result is the "slack" — how many positions each run can shift left or right.
A 10-cell row with a clue of [8] has a slack of 2: the run of 8 can start in position 1, 2, or 3. Cells 3 through 8 are guaranteed filled regardless of where the run starts. A 10-cell row with a clue of [1,1,1,1] needs 4 filled cells plus 3 gaps, so its slack is 3. Every run can shift by more than its own length, so the line yields no guaranteed cells at the start. Always work low-slack lines first and extract every certain cell before moving to higher-slack lines.
The Overlap Formula
The guaranteed cells in a constrained run are found by the overlap method. For a run of length R in a line of length L, the leftmost possible position for the run starts at cell 1. The rightmost starts at cell L-R+1. The overlap — cells that are filled in both the leftmost and rightmost placements — is the cells from (L-R+1) to R, if that range is non-empty. These cells are certainly filled. Mark them immediately and move on.
When a line has multiple runs, apply the overlap method to each run separately, accounting for the minimum space required by the other runs. With full candidate notation (marking cells as definitely filled, definitely empty, or unknown), the overlap method typically fills a significant portion of every tightly constrained line on the first pass.
Mark Empties as Hard as You Mark Fills
Beginners only fill cells; good solvers also mark known-empty cells, usually with a small X or a dot. Empties are just as informative as fills, because they wall off where a block can and can't go. Whenever you complete a row's clues, X out every remaining cell in it; those X's then constrain the crossing columns and crack them open. Treating empties as second-class is the most common reason a nonogram stalls.
Work the Crossings
The puzzle is solved by bouncing between rows and columns. A cell you fill from a row clue becomes a fixed fact for its column, and vice versa. Solve what a single line forces, then look at the crossing lines that line just changed, then back again. Distinctive lines — nearly full, nearly empty, or with one big number — are always your way back in when progress slows.
No Guessing Required
A proper nonogram has exactly one solution. Easier grids fall to line logic alone; harder ones sometimes need you to test a single cell and follow it to a contradiction, which is still logic, not guessing (our guide to what to do when no line solves walks through it). If you're stuck, you've usually missed an overlap or forgotten to mark some empties — scan for the line with the most constraint and work it again. Guessing risks corrupting the grid in ways that surface ten moves later as a contradiction you can't locate.
If you genuinely cannot find the next move, feed the clues into The Puzzle Solver’s free nonogram solver and compare its grid against yours — seeing which line you misread teaches you more than an abandoned puzzle does.
The fastest way to make any of this stick is to solve one. Hidden Heart is a good first grid, and Rainy Day Companion steps you up to medium once the basics feel automatic. Both print on one page with a fold-over answer key.
Bigger Grids and Colour Nonograms
The same logic scales to large grids and to colour nonograms, which add just one rule: two blocks of the same colour need at least one empty cell between them, but blocks of different colours can sit flush against each other. On big puzzles, don't try to hold the whole grid in your head — solve it region by region, leaning on whichever lines are most constrained, exactly as you would on a small one. The numbers may be longer, but every move is still one of the basics: find the overlap, mark the empties, and read across the crossings.
The Takeaway
Read the clues as ordered runs, start with the biggest numbers for guaranteed overlap, mark empties as diligently as fills, and bounce between crossing lines until the picture appears. It's a quiet, absorbing kind of logic — and the moment the hidden image resolves is genuinely satisfying.