Nonogram puzzles guide
How to Solve Nonograms: A Step-by-Step Guide for Beginners
Learn to solve nonograms with the overlap method, X marks and a simple routine. Includes worked examples and a full 5×5 puzzle solved one step at a time.
To solve a nonogram, look for lines where the clue is so big that some squares are filled wherever the block sits, fill those, mark squares that can no longer be filled with an X, then switch to the crossing lines and repeat. That loop — find certain squares, mark certain blanks, switch direction — solves every beginner puzzle and most intermediate ones.
This guide teaches the loop with small worked examples you can check by counting, then walks through a complete 5×5 puzzle. If you are brand new to the puzzle itself, start with what a nonogram is.
Read the clues correctly
Each row and column has a clue such as 3 1 2. It means: somewhere in this line there is a block of 3 filled squares, then a block of 1, then a block of 2, in that order, with at least one empty square between blocks. Row clues read left to right; column clues read top to bottom. A 0 means the line is completely empty.
In the examples below, # is a filled square, x is a square proved empty, and . is still unknown. The digits above each line number the squares 1 to 10 (0 stands for 10).
The overlap method: your first filled squares
Take a row of 10 squares with the clue 7. Push the block as far left as it can go, then as far right as it can go:
1234567890 leftmost #######... rightmost ...####### certain ...####...
Squares 4 to 7 are filled in both extremes, and every position in between covers them too. So those 4 squares are certain, even though you do not yet know where the block starts.
You do not need to draw both extremes each time. Use this shortcut:
- Add up the clues plus one gap between each pair. For
7that is just 7. - Subtract from the line length to get the slack. 10 − 7 = 3. Slack is how far each block can slide.
- Any block longer than the slack gives you squares. Block length minus slack = number of certain squares. Here 7 − 3 = 4.
It works with several clues too. Row of 10, clue 3 4: the minimum length is 3 + 1 + 4 = 8, so the slack is 2. The 3-block gives 3 − 2 = 1 certain square and the 4-block gives 4 − 2 = 2:
1234567890 leftmost ###x####.. rightmost ..###x#### certain ..#...##..
Notice that you compare each block with itself in the two extremes. The 3-block covers squares 1–3 on the left and 3–5 on the right, so only square 3 is shared.
Quick test: if the slack is 0, the line is completely determined. Row of 10, clue 2 3 3: 2 + 1 + 3 + 1 + 3 = 10, so the answer is ##x###x### with no thinking required. If the slack is larger than every block, the overlap method gives nothing yet — come back to that line later.
Mark empty squares with X
Filled squares are only half the job. Proving that a square is empty is just as valuable, because it cuts down the options for the crossing line. Use an X for every square you have proved empty. Three easy sources of Xs:
Finished lines
When every block in a line is in place, every remaining square is empty. Row clue 1 3 with #x### already filled in the first five squares of a 10-square row? The other five are all Xs.
Squares out of reach
Row of 10, clue 2, and square 5 is already filled. The 2-block must cover square 5, so it sits on squares 4–5 or 5–6. Everything else is out of reach:
1234567890 before ....#..... after xxx.#.xxxx
Zero clues
A 0 line is empty from end to end. Cross it out first — it gives a free X to every crossing line.
Solve a 5×5 puzzle with us
Here is a complete puzzle. Column clues are above the grid, row clues are on the left:
2 4 4 4 2
1 1 . . . . .
5 . . . . .
5 . . . . .
3 . . . . .
1 . . . . .
- Rows 2 and 3 say 5. In a 5-square row the slack is 0, so fill both rows completely.
- Row 4 says 3. Slack is 5 − 3 = 2, so the block gives 3 − 2 = 1 certain square: the middle one. Fill row 4, column 3.
- Columns 1 and 5 say 2. Rows 2 and 3 are already filled in both columns. That is the whole 2-block, so the other three squares in each column are empty. Put Xs in rows 1, 4 and 5 of columns 1 and 5.
- Columns 2 and 4 say 4. Slack is 1, so rows 2 to 4 are certain. Fill row 4 in columns 2 and 4.
- Row 1 says 1 1. Its first and last squares are already X, leaving exactly three squares for "1, gap, 1". That fits only one way: fill columns 2 and 4, X column 3.
- Finish the columns. Columns 2 and 4 now have rows 1–4 filled — that is their 4 — so row 5 gets an X. Column 3 has an X in row 1 and filled squares in rows 2–4; it needs 4, so row 5 must be filled. Row 5's clue of 1 is satisfied, and the puzzle is done.
2 4 4 4 2
1 1 x # x # x
5 # # # # #
5 # # # # #
3 x # # # x
1 x x # x x
A heart. Every step was forced by the clues; nothing was guessed. Notice the rhythm: rows gave us a start, columns turned that into Xs and new squares, and the remaining rows and columns fell quickly once enough was known. Bigger puzzles follow the same rhythm, just with more passes.
A routine that works on every puzzle
- Clear the freebies. Cross out every 0 line and fill every line whose slack is 0.
- Sweep all rows with the overlap method. Work out the slack once per line and fill any block longer than it.
- Sweep all columns the same way, now using the squares you just filled.
- After each new square, look at its crossing line. A fresh square near an edge or next to an X often decides a block on the spot.
- X anything out of reach, and X finished lines immediately. Empty squares are information; do not leave them blank.
- Repeat the sweeps until no line changes. On easy puzzles you will be done long before that.
When a full sweep in both directions changes nothing, it is time for the next layer of techniques — pushing blocks away from edges and Xs, joining and splitting fragments, and testing a "what if". Our advanced nonogram techniques guide covers each one with examples.
Mistakes beginners make
- Forgetting the gaps when adding clues.
3 4needs 8 squares, not 7. Leaving out the gap makes you see overlaps that are not there. - Filling squares "because it looks right". A square that would complete the shape you think you see is still a guess. Fill only what you can prove.
- Leaving empty squares unmarked. If you know a square is empty but do not X it, you will have to work it out again on the next pass — and the crossing line cannot use it.
- Ignoring the order of clues. In
1 3the 1 comes first. A lone filled square at the far right cannot be that 1. - Only working in one direction. Most progress comes from feeding rows into columns and back again.
Practicing in NonoPop
We built NonoPop to be a friendly place to learn. On first launch, the Play setup screen explains filled squares and X marks and offers a short tutorial on a 5×5 grid. Both helpers start off, so you get to practice the full logic yourself:
- Prevent incorrect moves stops a wrong fill before it lands. Turn it on while learning if you would rather not undo mistakes; leave it off to practice checking your own reasoning.
- Auto-mark empty squares adds the Xs to a row or column as soon as you complete it — the "finished lines" rule from above, done for you. Lines with a 0 clue stay manual.
Start with 5×5 and 10×10 grids in Quick Play, which makes a fresh puzzle in the size you pick, then step up to 15×15 with the Daily Puzzle. If you get stuck, Hint reveals one square (correcting a wrong one first), and Undo takes back your last move. Every NonoPop puzzle is checked by a solver, so it can be finished with logic alone and has one solution — if you are stuck, there is always a deduction waiting.
Frequently asked questions
Where should I start on a new nonogram?
With the biggest clues relative to their line length. Do the slack calculation for each line and start wherever a block is longer than the slack. Lines with a 0 clue or a slack of 0 are free starting points.
Do I have to mark every empty square with an X?
Not to finish — a puzzle is solved when the right squares are filled. But marking Xs as you go makes the crossing lines much easier, so it is worth the extra taps. In NonoPop you complete a puzzle by filling every correct square; Xs are optional.
What if no line has any overlap?
That happens on puzzles full of short clues. Look for lines touched by squares you already know, especially near edges, and use the reach rule to place Xs. If that still gives nothing, move on to the techniques in our advanced guide.
How long does it take to get good?
Most people are comfortable with 10×10 puzzles after a handful of games. The overlap shortcut becomes automatic quickly; reading two directions at once takes a little longer.