To solve a big nonogram, start with the lines whose biggest block is longer than their slack (the line length minus the clue and its gaps), start in the middle rather than on the border, and expect to come back to about half the lines more than once. On a 15×15 the three simple techniques (overlap, crossing out, edge forcing) usually stall about three quarters of the way through, and the rest needs joining and sliding blocks on the middle blocks of a clue.
That's what we found solving 1,000 15×15 puzzles and 1,000 10×10 puzzles from Poozee's Nonograms with a program that works the way a careful person does. Below are the numbers, then one real 15×15 solved from a blank grid to the moment it stalls and past it. If the technique names are new to you, our guide on how to solve nonograms explains each one with diagrams.
What changes on a 15×15
| 10×10 | 15×15 | |
|---|---|---|
| Squares | 100 | 225 |
| Average slack per line | 3.0 | 3.9 |
| Lines that give squares on a blank grid | 57.8% | 59.8% |
| Squares overlap settles on a blank grid | 41.2% | 35.6% |
| Line-by-line steps to finish | 24.3 | 46.9 |
| Lines worked on more than once | 25.9% | 48.8% |
| Puzzles where the simple techniques stall | 39.3% | 98.9% |
| Grid already settled when they first stall | 88.2% | 76.2% |
| Stalls per puzzle | 0.9 | 5.9 |
Three things stand out:
- The start is about as easy. A 15×15 has the same share of lines that give squares straight away, and each one gives more (5.7 squares on average, against 4.7). There are just more of them to find.
- The middle is longer. Nearly twice the steps, and nearly half the lines need a second or third look, because they only give up their last squares once the lines that cross them fill in.
- The end needs harder techniques. On a 10×10, spaces, edge forcing and overlap finish most puzzles on their own. On a 15×15 they almost never do.
How we measured
We made the puzzles with the game's own generator, seeds 1 to 1,000 for each size. Every puzzle the game deals has been checked by a line solver, so it can be finished one row or column at a time with no guessing. Then a program solved each one twice:
- Like a careful person: try the simplest technique on every row and column, and only reach for a harder one when nothing simpler works anywhere. A stall is a moment when overlap, spaces and edge forcing prove nothing on any line.
- One line at a time: each step, take the row or column that settles the most new squares and settle all of them. This counts the steps and how often each line gets worked on.
Our pictures are generated, so hand-drawn puzzles from books and apps will differ in the details, especially at the border (see below).
Where to start: the slack rule
On a blank line, add up the clue plus one gap between each pair of blocks, and subtract that from the line length. What's left is the slack: how far every block can slide. A block fills squares on a blank line only if it's longer than the slack, and it fills exactly (length minus slack) of them. That held for every one of the 30,000 lines in our 15×15s.
The rule matters more on big grids because lines have more room to slide. The average slack was 3.9 on a 15×15 against 3.0 on a 10×10, and 23.5% of 15×15 lines had a slack of 6 or more, against 12.3% on a 10×10. A lone block now needs to be 8 or longer to give anything:
On average 17.9 of a 15×15's 30 lines gave something on a blank grid, and every puzzle had at least 5. Scan for them first: clues that nearly fill the line, and single blocks of 8 or more.
Start in the middle, not on the border
The usual advice is to work the edges, and edge forcing really is a big technique on large grids. But on Poozee's 15×15s the border rows and columns are the last part to fall, because the pictures are thinner there: 47.8% of border squares are filled, against 65.4% inside. The generator smooths each picture: it fills a square when at least 6 of its 8 neighbors are filled and clears one with at most 1. A border square has only 5 neighbors (a corner has 3), so it can never be filled that way.
Thinner lines have more slack. On a blank grid a border line gave 1.0 square on average, against 3.8 for the other lines. And when half the grid was settled, 65.1% of the border was still open, against 44.0% of the inside. Start with the big clues in the middle, and let the border come to you.
A real 15×15, from blank to the first stall
Here's puzzle 14 from the generator. Rows are numbered from the top and columns from the left. In each diagram, blue squares and red Xs are the ones that step settled.
Step 1: overlap on every line
Columns 3 and 4 fit exactly: 10 + 1 + 4 and 5 + 1 + 9 both make 15, so there's no slack at all. Column 5 (9 4) has a slack of 1, and row 5 (9 3) a slack of 2. Overlap on all 30 lines settles 70 squares, 31% of the grid, a little under the 35.6% average.
Step 2: spaces and edge forcing until they run dry
From here, crossing out squares no block can use and pushing the first and last blocks in from the edges takes the grid from 70 squares to 174, 77% of it. Then none of the three simple techniques proves anything on any line. That's the first stall, close to the 76.2% average.
Step 3: joining in row 6
Edge forcing only ever moves the first and last block of a clue. What's left at a stall is usually a middle block, and row 6 has one: its clue is 2 5 3, and the 5 is in the middle.
Row 6 wasn't the only way on. At this stall, 14 of the 30 lines had a joining or sliding move waiting, and across all our 15×15 stalls the average was 8.6. You don't have to find one magic line; you have to stop looking only at the ends of the clues. If you press Hint in the game at this point, it points at row 6 and names "Joining and splitting".
Step 4: sliding in row 1
The solve stalled three more times. The last stall came at 191 squares, in the top row:
After that, the picture falls without another stall:
When the simple techniques run dry
On a 15×15, expect to stall: 989 of our 1,000 puzzles did at least once, 5.9 times on average, and the first stall came with 76.2% of the grid settled. On a 10×10 only 393 of 1,000 ever stalled, and not until 88.2% was done. When it happens:
- Look for middle blocks. Edge forcing has already done everything it can for the first and last block of every clue. A clue of three or more blocks has middle ones it never touches.
- Name the owner of each run. For each run of filled squares, ask which block of the clue it could belong to. When only one block fits, extend it, join it to the next run, or cap it with Xs, like row 6 above.
- Slide the whole clue. Push every block as far left as the marks allow, then as far right, and fill what the same block covers both times, like row 1 above.
- Then go back to the easy techniques. Every joining or sliding move adds a square to a crossing line, and that line usually has a simple move again.
Pro tip: On a big grid, count in fives. Poozee's board draws a heavier line after every fifth square, so square 12 is two past the second heavy line, and you never have to count a 15-square line one square at a time.
Expect to come back to every line
On a 10×10, about two lines in three only need working on once. On a 15×15 it's about one in two:
| Times a line was worked on | 10×10 | 15×15 |
|---|---|---|
| Never (its crossing lines filled it) | 6.9% | 1.9% |
| Once | 67.2% | 49.3% |
| Twice | 23.5% | 40.3% |
| Three times or more | 2.4% | 8.5% |
No line in any of the 2,000 puzzles needed more than 5 visits. That's the rhythm of a big grid: a line gives a few squares, waits for its crossing lines, then gives the rest. So whenever you fill or cross out a square, glance at the line that crosses it, and don't write off a line just because it gave nothing the first time.
Playing 15×15 on Poozee
- Screen size. The 15×15 button only appears on screens wider than 468 pixels, where its squares come out about 24 pixels wide. On a phone held upright you get 5×5 and 10×10; turn it sideways, or use a tablet or computer.
- Drag to fill long blocks. Drag along a row or column to paint several squares at once; the number in the top-left corner counts them as you go, which saves miscounting a 9 or a 10.
- Clues fade when a line is right. A row or column's clue turns gray once its filled squares match it, so you can see at a glance which lines are done.
- Hint teaches, Check catches. Hint settles one square and names the line and the technique, so at a stall it shows you where to look. Check marks any wrong squares in red, which is worth doing before a mistake spreads across 225 squares.
- Your puzzle is saved in your browser, so a big grid can wait until later.
Keep playing
- Play Nonograms: a daily 10×10, plus unlimited 5×5, 10×10 and 15×15 puzzles
- How to solve nonograms: every technique in this guide, with worked examples
- Nonograms for beginners: a 5×5 solved from a blank grid, one line at a time
- How to make a nonogram: draw your own and check it has exactly one solution
- Sudoku strategies, for the same "what can still fit here?" thinking with numbers
Frequently asked questions
Where should I start a 15x15 nonogram?
Work out each line's slack: 15 minus the clue's numbers and one gap between each pair. Any block longer than the slack fills squares right away. On our 15x15s, 17.9 of the 30 lines gave something on a blank grid, and the middle lines gave almost four times as much as the border.
Why can't I pick 15x15 on my phone?
Poozee only shows 15x15 on screens wider than 468 pixels, where its squares come out about 24 pixels wide, big enough to tap. Turn your phone sideways, or play on a tablet or computer.
Do big nonograms need guessing?
Not on Poozee: a puzzle is only kept if line logic solves it from a blank grid. But on 98.9% of our 15x15s the three simplest techniques ran out at least once, so you'll need joining, splitting and sliding blocks to finish.
How much harder is a 15x15 than a 10x10 nonogram?
It has 2.25 times as many squares and took 46.9 line-by-line steps on average against 24.3 in our tests. The bigger change is that 48.8% of its lines had to be worked more than once, against 25.9% on a 10x10.