Number Mosaic Strategy: Read Nonogram Clues Without Guessing (2026)

1. What the 36 puzzles actually are

Number Mosaic is a nonogram: every row and every column carries a clue, the clue lists the lengths of that line's filled runs in order, and the filled cells form a hidden picture. A clue of 3 1 in a line of ten means three filled cells in a row, at least one empty cell, then one more filled cell. A clue of 0 means the whole line is empty. There is no timer pressure, no score multiplier and no hidden information: the puzzle is the deduction.

The library is frozen at 36 puzzles, twelve in each tier:

A propagation round is one full pass over every row and then every column, narrowing each line with its own clue and the cells already known. The round count is the number needed to fill the grid from an empty board. Hard is not harder because it hides more information; it is harder because it starts with fewer decided cells and needs more rounds. More on that in section 3.

Each cell has three states: unknown, filled and marked (a cross meaning "I have proved this empty"). Only the filled cells are tested against the picture. Marks are notes, not answers; section 6 explains exactly what they do and do not do.

The timer starts on your first board action (paint, Hint or Check) and counts up. There is no time limit. Stars are three for a solve with no hint, two with one hint, one with two or more. Your best stars and time per puzzle, and your progress, stay in this browser. The size button cycles 5×5 → 10×10 → 15×15 → 5×5, the arrows move one puzzle at a time, and ?puzzle= pins a puzzle by number or tier, for example ?puzzle=hard or ?puzzle=25.

2. Read a line in one pass: four rules

Most of the game is decided by what a single line can tell you before you look at its neighbours. These four rules cover almost every opening move.

Rule 1 — a 0 clue empties the whole line. Mark every cell in it. This is free information: the line can never contain a filled cell, and every crossing line loses one candidate.

Rule 2 — a full-length run fills the whole line. If the clue is a single number equal to the grid size, every cell is filled. In 5×5 that is a clue of 5; in 10×10 a clue of 10; in 15×15 a clue of 15.

Rule 3 — a long run has a forced middle. A single run of length k in a line of length n has 2k − n cells that must be filled whenever 2k is greater than n. They sit in the middle of the line. The table below gives the exact cells, counted from the left:

This is the single most useful shortcut in the game. A 15×15 row with a clue of 10 already gives you five filled cells before you know anything else. A clue of 14 gives you thirteen and leaves only the two ends undecided.

Rule 4 — no slack means an exact layout. For a clue with more than one number, add the run lengths and the minimum one-cell gaps between them. If the total equals the line length, there is only one possible layout and you can fill and mark the whole line at once. Example: a 5-cell line with the clue 3 1 has 3 + 1 + 1 gap = 5, so the line is exactly XXX.X. A 10-cell line with 4 5 has 4 + 5 + 1 = 10, so it is exactly XXXX.XXXXX. There is nothing to guess.

The frozen library shows how often each shortcut appears. Across all rows and columns there are 15 easy, 8 medium and 7 hard lines with no slack at all — those lines can be completed from their clue alone. Another 32 easy, 22 medium and 10 hard lines have exactly one cell of slack, so they are not exact but are close. The rest need the crossing lines or the overlap rule. That is why the first pass does not finish a puzzle: it gives you a skeleton, not the picture.

One warning about the interface: when the filled runs you have drawn match a clue, the clue numbers get struck through. That mark means "your current filled runs match this clue", not "every remaining cell in this line is empty". Unknown cells are not runs, so a 5-cell line with clue 2 is struck through as soon as cells 1–2 are filled, even though cells 3–5 are still unknown. If you want to record that they are empty, mark them; do not read the strike-through as proof.

3. Why saturated lines beat guessing the middle

The tempting move when a board looks empty is to pick a cell in the middle and guess. In a build that is proved guess-free, that is the one move you never need. The measured shape of the library shows why working the saturated lines is faster.

I ran a pure one-line scan from an empty board: for each row and each column, list every placement of its clue that is consistent with the cells already known, and keep the cells that every placement agrees on. On easy boards that first scan already decides a median of 36% of the cells (range 8–52%). On medium it decides 34% (range 2–58%). On hard it decides 26% (range 15–38%). After one full row-then-column round — the first round the engine runs — the medians rise to 40%, 43% and 28% respectively.

Two things follow. First, a large part of every board is available before any cross-line reasoning: find it instead of guessing. Second, hard boards do not start with more information. They start with less, and they need 6–9 rounds to finish, against 3–5 on easy and 3–7 on medium. The difficulty is the length of the deduction chain, not the size of the grid.

A guess breaks that chain in a way the board cannot repair for you. If you fill a cell that the clues do not force, every later deduction from that cell inherits the assumption. The engine's Hint will eventually notice a contradiction, but only when the wrong fill contradicts a clue; a wrong fill that is merely unproven can survive for many moves and send you down a false branch. Undo is per stroke, so a bad drag is cheap to remove, but the reasoning you built on top of it is not. When something feels wrong, undo back to the last cell you could prove, not just one step.

The no-guess property is exact, not marketing. For every one of the 36 puzzles, repeated row and column narrowing fills the entire grid from the empty board, and an independent brute-force search counts exactly one solution. The generator rejected boards until both tests passed. If you are stuck, the correct conclusion is "I have not found the forcing line yet", never "I need to guess".

4. Zero clues and single-run lines are the skeleton

The clue distribution is uneven, and that is the strategy. Counted across all rows and columns of the frozen library:

A 0 clue is the strongest clue in the game: it empties a whole line at once. There are 20 / 34 / 46 of them, which is 16.7% / 14.2% / 12.8% of all lines. Mark them first. Every empty cell you record cuts a candidate from the crossing line, and the crossing line may then become exact.

A single-run clue is the next best thing. Single runs are the majority of all non-empty lines in every tier: 88 of 112 easy (78.6%), 137 of 206 medium (66.5%) and 164 of 294 hard (55.8%). A single run has a simple geometry: its start can slide, but the overlap in the middle cannot. That is why the long single runs in section 2 are the anchors of a 15×15 board.

The easy tier is almost entirely single-run and zero-clue lines: 88 single-run, 12 two-run, 20 zero, and no line with three or more runs. That is what makes 5×5 a warm-up. Medium introduces multi-run lines and a wider spread of filled density. Hard keeps the same maximum of four runs per line but has more long runs and many more crossing constraints. The line count grows from 120 to 240 to 360, while the number of rounds grows from 3–5 to 6–9; the board gets bigger, but the real jump is in how many times you have to revisit it.

5. Long clues, short clues, and the order of inference

The longest single run is 5 on easy, 10 on medium and 15 on hard — a hard board can contain a line that is filled end to end. The most clue numbers in one line is 2 / 4 / 4, and the total number of clue numbers is 132 / 320 / 547 (that count includes the single 0 entry on an empty line; the actual run lengths total 112 / 286 / 501). The lesson is simple: long runs are anchors, short runs are connectors, and a line with four short runs is the last place to start.

Use this order on every new board:

1. 0 clues — mark the line empty.
2. Full-length runs and no-slack lines — fill and mark the entire line.
3. Long single runs — apply the overlap table; fill the forced middle.
4. Lines with the most filled cells already — a line that is half solved is easier to finish than an empty one.
5. Crossing lines — after every fill, re-read the perpendicular clue. A single new filled cell can turn a column from undecided to exact.

Short clues are not useless; they are just weaker per line. A clue of 1 in a 5-cell line has five placements and no forced cell. A clue of 3 has one forced cell. A clue of 3 1 in five cells is exact because there is no slack. The number of runs matters as much as the length of the runs: a line with four numbers has many ways to distribute the gaps, so save it until its crossings have narrowed it.

When a line has several runs and some slack, do not enumerate placements in your head unless the line is short. Let the crossings do the work: fill the forced parts of the long runs, mark the cells that are certainly empty at the ends, and come back when a crossing line fixes one of the gaps. The 15×15 board is designed for this loop; it is not designed to be read in one glance.

6. Marks are notes, not facts

The Mark tool puts a cross in a cell. It is the most misunderstood tool in the game, so here is the exact behaviour of the shipped build.

• In the win test, a mark counts as empty. The game compares only filled cells with the picture. A marked cell and an unknown cell are both "not filled". Marking a cell that should be filled does not create an extra error; it simply leaves the puzzle unsolved.
• In Check, a mark counts as not filled. Check compares every cell with the picture and counts both missing and extra filled cells. A marked cell that should be filled is counted as missing. Marks do not lock an answer in, and they do not hide a mistake from Check.
• In Hint, a mark is invisible. The narrowing behind Hint treats only filled cells as known; marks are treated as unknown. Marking cells does not make the Hint smarter and does not change which cell it reveals.
• A struck-through clue is not a proof of empty. As explained in section 2, the clue is struck through when your filled runs match it. The remaining unknown cells are still unknown. Mark them if you want to record that they are empty.

So what are marks for? They are for you: they record a deduction you have already made, so you do not re-scan the same line, and they make the empty cells visible at a glance. Use them generously on cells you have proved empty by a 0 clue, a no-slack layout or a crossing. Do not use them on cells you are only guessing about; a wrong mark is not an error in the win test, but it can mislead your own later reading and it will show up in Check as a missing filled cell.

A good habit is "fill what is forced, mark what is excluded, leave the rest alone". The board then shows three kinds of cells honestly: black (proved filled), crossed (proved empty), and blank (still unknown). If you mark a cell before you can prove it, you have turned a question into a false answer, which is worse than leaving it blank.

7. The Hint is a narrowing tool, not an oracle

The Hint button has two paths in the shipped build, and knowing both changes how you spend it.

1. Forced path. Hint takes the cells you have actually filled, runs the same line-by-line narrowing a person would, and looks for a cell that every consistent placement agrees on. If it finds one, it reveals that cell (filled or empty), highlights it, and adds one to the hint count. This is real deduction from your position; it never reads the stored picture on this path.
2. Fallback path. If your current fills force nothing new, Hint picks the first unknown cell in reading order and reveals its value from the stored picture. It does not explain why, because there is no line-logic reason. This is the path that gives a hint its "oracle" reputation.

If your filled cells contradict the clues, Hint refuses: it says some fills disagree, asks you to undo or clear them, and does not add to the hint count. If every cell is already filled or marked and the board is still wrong, it also does nothing.

Every successful press counts, including a fallback press. Stars are 3 with zero hints, 2 with one, 1 with two or more. Restart clears the board, the timer and the hint count, so restarting is the way to protect a three-star attempt; your saved best is not overwritten by a worse run. The best record compares stars first and time second: a 3-star 5:00 beats a 2-star 1:00, and a 2-star 1:00 beats a 2-star 2:00.

The practical rule is: fill everything that is forced before you press Hint. If you press it on an empty board, you will often get the fallback cell, which spends a hint without teaching you a line. If you press it after a full scan, you are much more likely to get a forced cell that extends your reasoning. And if Check says the board has disagreements, do not press Hint — find the wrong stroke first.

8. A practice loop that transfers

A five-step loop works on all three sizes:

1. Scan for zeros and exact lines. Mark every 0 clue; fill every full-length run and every no-slack line.
2. Apply overlap to long single runs. Use the table in section 2. On 15×15, a run of 8 or more is worth checking immediately.
3. Re-read the crossings. Every fill changes a perpendicular line. Do a full row pass, then a full column pass, then repeat.
4. Check before Hint. Check tells you whether the picture is already right; if it is not, it tells you how many cells disagree, not which. Use that number to decide whether to keep deducing or to undo.
5. Only then use Hint. One hint is a two-star solve; two hints is one star. If you are chasing three stars, restart rather than spend a second hint.

For practice, start at 5×5 and aim for three stars on all twelve. The easy tier has no line with more than two runs, so it trains the two core habits: zero/exact lines and the overlap rule. Move to 10×10 when you can finish a 5×5 without marking a guess. Move to 15×15 when you can finish a 10×10 with at most one hint. The hard tier is a patience exercise: 225 cells, 6–9 rounds, and a board that will look stuck for a while before a crossing unlocks it.

Use ?puzzle= to replay a specific puzzle. Progress and best times are stored per puzzle in this browser, so a replay is a fair comparison. The timer starts on your first action, so if you want a clean time, read the board before you paint. On a phone, drag painting is the fast way to fill a run; a 15×15 cell is about 21px wide on a 390px screen, and the buttons stay at least 34px tall, so the board is playable without zooming.

9. If you get stuck: a checklist

Work down this list before you press Hint or guess:

1. Did you mark every 0 clue? There are 20 / 34 / 46 free lines in the three tiers.
2. Did you fill every no-slack line? There are 15 / 8 / 7 lines that are exact from their clue alone.
3. Did you apply overlap to every single run longer than half the line?
4. Did you re-read the crossings after your last fill, or are you still looking at the board from two moves ago?
5. Did you mistake a struck-through clue for proof that the rest of the line is empty?
6. Did you mark a cell that should be filled? Check counts it as missing; the mark is not an answer.
7. Did you make a guess that has not contradicted yet? Undo back to the last cell you could prove.
8. If you have done all of the above, press Check once. If it reports disagreements, undo the last stroke and re-scan. If it reports zero, the puzzle is already solved.
9. Only after that, use Hint once. If you are chasing stars, restart instead of spending a second hint.

FAQ

How do you solve a nonogram without guessing?

Use the cells the clues force. Start with 0 clues, full-length runs and no-slack lines, then apply the overlap rule to long single runs, then re-read the crossing lines. Every puzzle in Number Mosaic is proved to fill from row and column narrowing alone, and an independent search finds exactly one solution. If you are stuck, a forcing line is missing from your scan, not from the puzzle.

What does a 0 clue mean in a nonogram?

The whole line is empty. A clue of 0 is not "no clue"; it is a fact that the line contains no filled cells. Mark every cell in that row or column. The frozen library has 20 zero lines on easy, 34 on medium and 46 on hard.

How do you read nonogram clues?

Each number is the length of one filled run, in order, with at least one empty cell between runs. A clue of 3 1 in a line of ten means three filled cells, at least one empty, then one filled cell. A clue of 0 means the line is empty. A single number equal to the line length means the whole line is filled.

What is the overlap rule in a nonogram?

A run of length k in a line of length n forces 2k − n cells in the middle when 2k is greater than n. In a 15-cell line, a run of 10 forces cells 6–10; a run of 14 forces cells 2–14. In a 10-cell line, a run of 7 forces cells 4–7. The rule works because the run cannot slide far enough to avoid the middle.

Do marks count as mistakes in Number Mosaic?

Not in the win test, but they are not a free answer either. The win test looks only at filled cells, so a mark counts as empty. Check counts a marked cell that should be filled as missing. The Hint ignores marks entirely: its narrowing treats only filled cells as known. Marks are notes for your own reading, not facts the game uses.

Does the Hint use the solution?

Sometimes. If your filled cells force a cell, Hint reveals that forced cell by line logic and does not read the stored picture. If nothing is forced, it falls back to the first unknown cell in reading order and reveals its value from the stored picture, without a reason. Every successful press counts toward the star rating.

How many puzzles are in Number Mosaic?

36: twelve 5×5, twelve 10×10 and twelve 15×15. They are numbered 1–36 in that order. Use ?puzzle=hard to start on the first hard puzzle or ?puzzle=25 to pin a specific number; an invalid value falls back to puzzle 1.

How are stars awarded?

Three for a solve with no hint, two with one hint, one with two or more. Undo does not affect stars. Restart clears the hint count, so a restart can protect a three-star attempt. Your best record compares stars first, then time.

Is there a timer or a time limit?

There is a timer, but no time limit. It starts on your first board action — paint, Hint or Check — and counts up. Your best time per puzzle stays in this browser. Nothing ends the game except a correct picture or a restart.

Can I play Number Mosaic on a phone?

Yes. Tap a cell to paint it and drag along a row or column to paint a run; one press-release is one undo step. On a 390px-wide screen a 15×15 cell is about 21px, and the buttons are at least 34px tall. There is no download and no sign-up.