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Nonograms puzzle solution
This is an example of a completed Nonogram puzzle. A Nonogram puzzle consists of a grid with clues along the top and the left side.
Your aim in these puzzles is to colour the whole grid in to purple and white squares. At the top of each column, and at the side of each row, you will notice a set of one or more numbers. These numbers tell you the runs of purple squares in that row/column. So, if you see '5 6', that tells you that there will be a run of exactly 5 purple squares, followed by one or more white squares, followed by exactly 6 purple square. There may be more white squares before/after this sequence.
Nonograms puzzle
This is an example of a starting Nonogram grid. This particular puzzle is 20x20 in size. As a general rule you can assume that the bigger the grid, the harder the puzzle.
The starting point in any size puzzle will be to look for row/columns that will be mostly purple squares. Halfway down the left-hand side is the clue '7 9', i.e. we will have 7 purple squares, a break of one or more white squares, and then a further 9 squares. There's only a limited numbers of ways this combination can be arranged in to the grid. Let's look at those.
These are the two extremes for that row. You will see that there is a great deal of overlap between the two extremes of possibility for this row, so we can fill those in purple. We don't know exactly where those purple blocks will start/end, but we know where some of them will go.
Nonograms puzzle
We now have this as our current work-in-progress. Notice that there is some overlap between the two extremes in the middle of the grid, but that white cell in the middle is free to move between those two extremes. It could also be more than just a single white square - all 4 white squares could be in the middle for example.
There's a few more opportunities for this kind thinking in this puzzle. We have three columns that are interesting to us:
  1. The column with the clues of '4 15'.
  2. The column with the single clue of '13'.
  3. The column with the clue of '12 1'.
You may notice that there is only one way to satisfy the first of our columns - so we can completely fill that column in. We can also apply the same process to our other two columns.
Nonograms puzzle
There are a few other rows/columns that we can apply a similar technique with, but we will start seeing diminishing returns fairly soon with this technique.
Look at the row with the 4 highlighted squares. The first number in the clue for that row is '8'. The first purple block in that row gives an 'anchor' for that '8', and gives two extremes for that block of 8. It can either start in the cell in the row, or the latest it can start is on the first purple block. For both those extremes, and everything in between, those highlighted are going to be purple.
We can apply the same line of reasoning to many cells in the same way.
Nonograms puzzle
By applying the same line of reasoning to other we arrive at this point. Look now at the highlighted cell. The first clue for this row is a '3', there is no way for the highlighted cell to be purple because of where the existing purple cells are; if this cell was purple it would create a first block of 4+ cells, which wouldn't satisfy the first clue. This cell then must be white.
We have made great progress in solving this puzzle. You now know the main lines of reasoning for solving Nonograms, happy puzzling!

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