Deduction puzzle

Nonogram

Numbers down the side, numbers across the top, and a picture hidden between them. Every grid here is proved solvable by logic alone before you ever see it.

  • 5×5–10×10Grid sizes
  • 1–12 minTypical time
  • No guessingGuaranteed
Logic workoutNonogram
Practice

How to play

Read the clues. Reveal the picture.

Each number beside a row or above a column is a run of filled cells, in order. A clue of3 1 means three filled cells, then at least one gap, then one more filled cell.

  1. 1
    DeduceFind cells that must be filled in every possible arrangement.
  2. 2
    MarkTap once to fill, again for a cross, again to clear.
  3. 3
    Cross outMarking known-empty cells is what makes the next deduction visible.

Every puzzle here is solvable by pure logic. The generator throws away any grid that would need a guess, so if you are stuck there is always a deduction you have not found yet.

Choose your levelLarger grids mean longer chains of deduction before the picture appears.Checking saved progress…
Choose Nonogram difficulty
No time limit

A nonogram is the rare puzzle that pays you at the end. Every other grid puzzle finishes with a grid; this one finishes with a picture that was there the whole time, encoded in two lists of numbers you had no reason to trust until it appeared.

How to play a nonogram

Each number beside a row, or above a column, is the length of one unbroken run of filled cells, listed in the order those runs appear. A clue of 3 1 means three filled cells together, then at least one empty cell, then exactly one more filled cell. The gaps between runs can be any size, and there may be empty cells before the first run and after the last.

You are not guessing where the runs go. You are finding the cells that must be filled — or must be empty — in every arrangement the clue still allows. Marking the empty cells is not optional bookkeeping; it is usually what makes the next deduction visible.

Overlap is the opening move

On a 10-wide line, a clue of 8 can start at column 1, 2 or 3. Slide it to both extremes and the cells covered in both cases must be filled — six of them, before you have looked at anything else.

The techniques that actually solve grids

  1. Overlap the big clues first. Any run longer than half the line forces cells. Push it as far left as it will go, then as far right, and fill everything covered both times.
  2. Work the line, not the cell. Ask “what does this clue allow?” rather than “is this cell filled?”. A single line often gives up three or four cells at once.
  3. Cross out relentlessly. A line whose runs are all placed has every remaining cell empty. Those crosses are what let the crossing lines resolve.
  4. Use the edges. A run touching the first or last cell has nowhere to slide, so it is fully determined immediately.
  5. Count what is left. If a clue’s runs plus their minimum gaps exactly fill the line, the whole line is forced with no freedom at all.
  6. Switch lines when stuck. A stalled row usually means a crossing column has information you have not extracted yet. Rotate your attention rather than staring.

Why you will never need to guess

This is the part most nonogram generators get wrong, and it is worth being precise about. Producing a grid with exactly one solution is not enough. A puzzle can have a single valid answer that is only reachable by picking a cell, assuming it is filled, following the consequences for twenty moves, hitting a contradiction, and backtracking. That is a search, not a puzzle, and it is miserable to play.

So the requirement here is stricter. Every grid is generated, its clues are derived, and then a line solver attempts it from blank — repeatedly narrowing each row and column to the cells that all remaining arrangements agree on, and never branching. If that process stalls with even one cell undecided, the grid is discarded and a new one generated. Only puzzles that fall out of pure deduction are published.

The same solver then has to reproduce the original solution exactly, which proves uniqueness as a by-product. If you are stuck on a grid here, there is a deduction available that you have not found — that is a promise the generator enforces, not a hope.

What the difficulty levels change

Only the grid size, which is the honest variable. A 5×5 rarely needs more than one or two chained deductions. An 8×8 usually requires you to alternate between rows and columns several times before the picture resolves. A 10×10 has longer clue lists, more places for each run to sit, and chains of deduction that can run four or five lines deep before paying off.

Fill density stays around 55% at every size, which keeps clues informative — very sparse or very dense grids produce clue lists that are either trivial or nearly useless.

Nonogram difficulty comparison
LevelGridCellsTypical timeGuessing needed
Easy5×5251–3 minutesNever
Standard8×8643–8 minutesNever
Hard10×101005–12 minutesNever

How the Nonogram score works

Completion supplies 85% of the score and solving pace the remaining 15%. There is no time limit — the timer runs, but it only affects the score once the grid is actually finished, and an exact solution scores strongly however long it took.

Completion is measured as the average of two figures: how many filled cells you found, and how many empty cells you correctly left alone. That pairing matters, because the obvious way to cheat a completion measure is to fill every cell in the grid, which finds all the filled ones by brute force. Under this measure filling everything scores zero, filling nothing scores zero, and filling at random scores zero. Only actually telling the two apart earns anything.

Cells you cross out are a memory aid and are never scored — crossing out is a solving technique, not an answer. Your result does report how many cells you filled wrongly during the attempt, as feedback about whether you were deducing or guessing.

Nonograms, Picross, and the other names

The same puzzle circulates under several names. Nonogram is the most common in print. Picross comes from the Nintendo series that popularised it on handhelds. You will also see griddler, hanjie, paint by numbers and Japanese crossword — all describing the same rules. The format was independently devised in Japan in the late 1980s, and the name “nonogram” derives from Non Ishida, one of the two people credited with inventing it.

Common nonogram mistakes

Not marking the empty cells

Players new to nonograms often fill cells and leave everything else blank. The crosses are half the information: a line cannot be resolved until you know which cells are ruled out.

Guessing when stuck

On these grids a guess is never necessary, so a guess is always a shortcut past a deduction you have not made. Change lines instead — the information is usually in a crossing column.

Reading clues as totals

2 3 is not five filled cells in a row. It is a run of two, a gap, then a run of three, in that order.

Forgetting the order is fixed

Clues are listed in the order the runs appear along the line. A clue of 1 4 can never mean the four comes first.

Nonogram questions

Is every puzzle really solvable without guessing?

Yes, and it is enforced rather than assumed. Each candidate grid is solved from blank by a line solver that only ever deduces — it narrows every row and column to the cells all remaining arrangements agree on, and never branches or backtracks. If that stalls with any cell undecided, the grid is thrown away and another is generated. Only grids that survive that test are published.

Do the pictures mean anything?

No, and we would rather say so. The grids are generated from a seed, so the finished picture is an abstract pattern rather than a drawing of something. Hand-authored nonograms in books often depict recognisable objects; these do not, and pretending otherwise would be dishonest. What you get instead is a fresh puzzle every time rather than a fixed set.

Why can I not clear a wrong fill without it counting?

You can clear it — tap a third time, or press Backspace. The grid does not lock. But wrongly filled cells are counted for the whole attempt and reported at the end, because that number is the honest difference between deducing and guessing. It is shown as feedback and does not directly reduce your score.

Can I play with a keyboard?

Yes. Arrow keys move around the grid, Enter or Space cycles a cell between blank, filled and crossed out, and F and X set filled and crossed directly. Backspace or Delete clears a cell.

Is Nonogram in the Daily Brain Workout?

No, and it is unlikely to be. The Daily needs stations of predictable length, and a deduction puzzle takes forty seconds if you spot the opening move and considerably longer if you do not. That variance is fine for standalone play and wrong for a five-station circuit, so Nonogram sits alongside Binary Grid and Tower Transfer as a standalone Logic and Planning game.