Nonograms: a practical guide with interactive examples

This is a nonogram

It’s an image puzzle.

Your goal is to reveal the hidden pixel art image.

You are guided in that task by the numbers around the board.

Basic moves

The numbers show how many cells should be filled in a given row.

For example, in a row like this you should fill four cells:

4

4

Try it - tap the squares below.

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And in a row like this you should fill one cell:

1

But wait: which one? We don’t know yet.

This is a very important technique: only fill cells when you’re certain; no guessing.

In our case, we could fill one cell in four different ways:

1

1

1

1

We’d have to guess the correct one.

If our guess is wrong, we’d encounter inconsistencies later on.

Let’s not do that.

Instead, we search for a different row where we don’t have to guess.

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All rules that apply to rows, apply to columns too.

	4

	4

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When there are two or more numbers, this means there will be two or more groups of filled cells.

And that they will be separated by at least one empty cell. Like this:

2	1

2	1

Try solving the puzzle below:

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We mark cells that will definitely be empty with a cross.

For example, if we saw a zero, we could mark all cells as empty.

0

0

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Or if we saw a row where all required cells have already been filled.

Then we could mark remaining cells as empty.

1

1

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Or if we saw a completed group - then we could put a ‘cross’ at each of its ends¹.

2	2

2	2

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That’s all of the basic techniques; you’re ready to solve a nonogram!

Give it a try below if you want.

Tap to fill a cell, drag to fill multiple cells, crosses will be inserted for you automatically.

Let’s try one more.

You can now place crosses yourself too.

Use the button below to toggle between filling cells and placing crosses.

Congrats, you’re now familiar with nonograms!

What follows is a list of nonogram solving techniques and more examples.

Browsing this list should be helpful for players of all levels.

For even more puzzles, download my app.

Or find more nonograms elsewhere².

List of techniques

Note

Each practice section assumes understanding of the accompanying technique and all earlier techniques.

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Fill row

4

4

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Fill space

4

4

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Fill row with multiple groups

2	1

2	1

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Crosses in an empty row

0

0

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Crosses in a completed row

1

1

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Crosses around completed groups

2	2

2	2

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Crosses in narrow spaces

3

3

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Crosses in narrow spaces with multiple groups

1	2

1	2

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Group joining

5

5

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Group splitting

2	2

2	2

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Group expanding next to border

3	1

3	1

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Group expanding next to crossed cell

1	2

1	2

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Crosses in unreachable cells

3

3

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Overlapping

4

4

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Overlapping multiple groups

3	1

3	1

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Examining all valid solutions

This is a general concept, both a technique and a property of the game itself:

In a slightly reworded way, it works with crossed out cells too; that is:

These can be applied in a number of scenarios.

Sometimes the techniques described above will be simpler and perhaps a better fit.

In particular “overlapping” will often be easier to apply.

But in other cases examining all valid solutions will be a more flexible approach.

Let’s look at practical examples.

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Quasi overlapping

4

4

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Quasi overlapping, multiple groups

3	1

3	1

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Quasi unreachable cells

3

3

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Quasi overlapping and group expansion

3

3

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Quasi overlapping, multiple groups and expansion⁵

We could approach this as before and check all valid solutions:

1	3

1	3

Alternatively, we could “split” the row alongside the crossed cell and look at valid solutions for each clue:

1	3

1	3

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Element size pinpointing

1

1	1	1

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X+1 empties

1	2

1	2

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X+1 empties, larger

2	3

2	3

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Minimal expansion

2	3

2	3

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Empty cells in all possible group matches

2	1

2	1

Note that the fourth cell will either belong to the final 1 group (and then there will be no filled cells after that), or to the first 2 group (in which case the group would be expanded and the sixth cell would be empty to keep the group separate). In both cases the sixth cell is empty and it is safe to put a cross there.

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Testing

Sometimes we don’t have enough information to find the next filled cell.

Like in this nonogram:

	1	1	1	2	2	1	1
2
3
4

We can use all of the earlier techniques and get to this state:

	1	1	1	2	2	1	1
2
3
4

But now we’re stuck. What next?

We can do placement testing.

We pick a cell:

	1	1	1	2	2	1	1
2
3
4

And we test what happens when we fill it.

	1	1	1	2	2	1	1
2
3
4

	1	1	1	2	2	1	1
2
3
4

	1	1	1	2	2	1	1
2
3
4

	1	1	1	2	2	1	1
2
3
4

	1	1	1	2	2	1	1
2
3
4

We ran into an error!

We see a cell that should both:

• be empty, because of a 1 column clue, and
• be filled, because of a 2 row clue.

This means that the original cell can’t be filled.

If it is then we run into an inconsistency; we just tested that.

So we can safely put a cross there.

	1	1	1	2	2	1	1
2
3
4

It also works with placing crosses.

You can experiment with that puzzle in the practice section and continue solving it.

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Edge logic

This is a special case of testing:

It’s testing alongside edges, while looking at related clues.

It’s useful because it’s fast and doesn’t take many steps.

Consider this nonogram:

	2	2	2	1
2
2
1
2

Imagine we fill a cell along one of the edges:

	2	2	8	8
8
8
1
2

	2	2	8	8
8
8
1
2

	2	2	8	8
8
8
1
2

We ran into an inconsistency very quickly.

That’s because alongside edges there can be many opportunities to expand groups⁶.

So now we can safely put a cross in the original cell.

	2	2	2	1
2
2
1
2

As an example, let’s continue with edge logic (even though at this point overlapping would be easier).

	8	2	2	8
8
8
1
2

	8	2	2	8
8
8
1
2

	8	2	2	8
8
8
1
2

We run into another inconsistency just as quickly - we could place another cross.

You can experiment with that puzzle in the practice section and continue solving it.

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Epilogue

You’ve reached the end!

And you solved 0 out of 22 puzzles on this page.

I hope you enjoyed it, and that you’ll complete even more nonograms in future.

Happy solving!

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Special thanks to reader Motor_Raspberry_2150 for providing examples about X+1 empties, minimal expansion, element size pinpointing and empty cells in all possible group matches.

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