How to Solve Nonograms: A Beginner's Guide with a Worked Example

Short answer: a nonogram is a grid with numbers beside every row and column. Each number is the length of a run of filled cells in that line, in order, with at least one empty cell between runs. You solve it by working out which cells must be filled and which must be empty, one line at a time, until a hidden picture appears. You never need to guess.

On this page

1. The rules in 30 seconds
2. Reading a clue
3. A worked example: solving a 5×5 nonogram
4. Five habits that make every nonogram easier
5. The same rules, in three dimensions

Nonograms go by a lot of names: picross, griddlers, hanjie, paint by numbers, Japanese crosswords. The rules are the same under every name. (If you are curious where all those names come from, see What Is a Nonogram?.) This guide teaches the rules, then walks through a complete puzzle so you can see every deduction.

The rules in 30 seconds

1. Each number is a run of filled cells. A clue of 4 means four filled cells in a row, side by side.
2. Several numbers mean several runs, in order. 3 1 means a run of three, then a run of one, reading left to right (or top to bottom for columns).
3. Runs are separated by at least one empty cell. The gap can be longer than one cell, and there can be empty cells at either end of the line.
4. A clue of 0 means the whole line is empty.

That's it. Most apps let you fill a cell or mark it with an X to show it is definitely empty. Use the X liberally: knowing where the gaps are is half the puzzle.

Reading a clue

Here is one six-cell row with the clue 3 1. There are only three ways it can work, and one common mistake:

Clue 3 16 cellsFitsFitsFitsWrong order

Look at what every valid version has in common: cells 2 and 3 are filled in all of them. That means you can fill those two cells right now, without knowing which arrangement is correct. Finding cells that are the same in every possible arrangement is the whole game. Everything else is a faster way of doing it.

A worked example: solving a 5×5 nonogram

Here is a small puzzle. Clues for each column are stacked above it; clues for each row are to its left. Try it yourself first if you like, then follow along.

24442115531

Step 1: fill the full lines

Rows 2 and 3 both say 5 in a row that is five cells long. There is only one way to fit a run of five into five cells, so both rows are completely filled.

24442115531

Step 2: use the overlap in the long columns

Columns 2, 3 and 4 each say 4. A run of four in five cells either starts at the top (rows 1–4) or one cell down (rows 2–5). Either way, rows 2, 3 and 4 are filled. Rows 2 and 3 already are, so the new information is row 4 in each of those columns.

24442115531

This is called the overlap method, and it is the single most useful technique in nonograms. The strategy guide covers it in depth, including how it works when a line has several clues.

Step 3: cross off the finished lines

Now some lines are already complete, and anything left in them must be empty:

• Row 4 says 3 and already has three filled cells in a row. Its two end cells are empty.
• Column 1 says 2 and already has two filled cells (rows 2 and 3). Rows 1, 4 and 5 of that column are empty.
• Column 5 is the same: X out rows 1, 4 and 5.

2444211××553××1××

Step 4: solve the top row

Row 1 says 1 1: two single cells with a gap between them. Its two end cells are crossed out, so only the middle three cells are left. The only way to fit “one, gap, one” into three cells is filled, empty, filled.

2444211×××553××1××

Step 5: finish the columns

Columns 2 and 4 now have four filled cells (rows 1–4), which completes their 4, so their bottom cells are empty. Column 3 has its top cell crossed out, so its run of four must be rows 2–5, which fills the bottom-middle cell. Row 5's clue of 1 checks out. Solved: it's a heart.

2444211×××553××1××××

Notice that we never guessed. Each step used one line's clue plus whatever the crossing lines had already proved. Bigger puzzles work exactly the same way. There are just more lines to cycle through.

Five habits that make every nonogram easier

1. Start with the big numbers. A clue equal to the line length fills the line; any single clue longer than half the line gives you overlap cells. Add up multi-number clues plus their gaps: if the total is close to the line length, the line is nearly determined.
2. Mark empties, every time. An X is information. Many deductions are only possible because you know where a run can't go.
3. Sweep, don't stare. Go through every row, then every column, then repeat. When one cell changes, its crossing line may suddenly have a new deduction.
4. Finish lines out loud. The moment a line's clue is satisfied, cross out everything else in it. This is the move beginners skip most often.
5. If you're unsure, leave it blank. Only fill a cell you can prove. A wrong guess can quietly poison the rest of the puzzle.

The same rules, in three dimensions

Once flat nonograms click, the 3D version is a natural next step. In a 3D nonogram (the style made famous by Picross 3D), you start with a solid block of cubes instead of an empty grid. Each clue sits on the face of a cube and counts how many cubes in that line belong to the hidden shape.

In Carve, our 3D nonogram game for iPhone, the same three ideas carry over directly:

• A 0 means chip the whole row: nothing in it belongs, just like a zero clue in 2D.
• A number equal to the row's length means mark every cube: the full-line rule from Step 1.
• Marks under the number tell you how many groups: a bar means the cubes form one unbroken run, two dots mean exactly two separate groups, three dots mean three or more. That replaces the multi-number clues of flat nonograms.

Chipping a cube is the 3D version of an X; marking a cube is the version of filling it in. Carve's first lessons walk through exactly these rules on tiny puzzles before you take on the full chapters.