How to Solve Nonogram Puzzles
Nonograms are named for Japanese graphic editor Non Ishida, who once won a contest in 1987 to beautify the night cityscape of Tokyo with an idea to turn window lights in skyscrapers on or off to form pictures. A puzzle designer named Tetsuya Nishio invented Oekaki-Logic, which used the same concept of on-off artwork in cells. The puzzle went through several titles until the name Nonogram appeared in The Sunday Telegraph in 1990, named by UK supplier James Dalgety, to honor Non Ishida.
Your goal is to create a picture in the grid using the number clues on the left and top to determine which cells must be filled in.
A clue number tells how how many cells must be colored in that row or column, all as a single group. For example, if there is only a number 6 in a column of 10 cells, there must be a contiguous set of 6 cells all filled in somewhere in that column, and the other 4 must be empty.
If there is more than one clue number, as shown here, that means there must be a group of cells for each number, with at least one empty cell between groups.
In the absence of other information, any one of these could fit the clue of 2-2 in a set of ten cells, among many others. This ambiguous nature is what presents the challenge of a nonogram, and is why you need both vertical and horizontal clues to solve the grid.
The two basic techniques are to look for extremes, where you can find known cells regardless of which end the group starts at, and to mark out known blanks using an X.
First, we will mark known empty cells in the rows and columns that had no clues (some puzzles may show a 0 instead of being blank).
Next, let’s take this top row as an example. We know we have to have a continuous group of 6 cells filled in. If we were to start at the beginning, we can count out 6 cells in blue. If we started at the end of the row and counted backward, we would have a group starting with the yellow squares.
The green squares show where both groups would have cells. Any set that started somewhere in the middle of the row would also have cells filled in here, so the green cells must be marked in no matter what.
Notice that the top clue in each of these columns was a 1. Because we have now filled out the top cell in each of the columns, we have fulfilled the first clue, which means that the empty cell below them must be blank. For the columns with multiple clues, we don’t know where the other filled in cells will be for the moment, although in the column that only had a single clue, we know the rest of its cells will be blank..
After filling in those Xs, we can see that the clues for the second row, a pair of 2s, can fill in all the remaining cells in the row, so we will do that now.
Next, take a look at this column. The clue shows that there is a single group of 6.
We know it can’t be at the bottom of the column, because there are only two spaces. Look for situations like that, where the available group can’t fit spaces blocked off by an X or the border. It will let you place Xs to eliminate more impossible places.
Also, we have a known cell filled in. We can’t be sure if it is the first or second block in the group, but we can see that if we started the group in the earliest possible position, it would have to extend down through the shaded cells below the known block.
This means we can definitely fill those four cells, but we’ll leave the top one unshaded for now.
The final basic technique is to look for places where you have a known cell and only one clue remaining. Here, we have a known filled cell for a column clue of 2.
At maximum, the filled group will either extend upward into the green cell, or downward into the pink cell. It cannot possibly reach any other empty cell in the column, so we know that all of them must be blank, and we can mark them with an X.
Now, let’s combine a few techniques.
In the columns with the clues 3 and 4, they cannot fit in the bottom two rows, so we can X out those spaces. We also could have done this because those rows each had a clue of 2, and they were single cells in the rows which could not have contained two filled blocks.
Also, we have known cells filled near the top. The light blue shaded cells show how far they would extend if those filled groups began in the earliest possible cell, so we know the blue cells below the filled one must be filled.
Next, the pink cells show the maximum extent of those groups if they began at the known filled cell, so we know that any cells below that point must be blank, so we can place more Xs.
Finally, in the bottom rows, we have three open cells for a clue of 2. Light red cells show the earliest possible beginning point, yellow the latest possible end point, and the orange cells must be filled by either possibility, so we know those must be filled.
Looks like we completed a few clues with that last set of known filled cells. With pen and paper, you’ll typically cross out clues for groups you’ve completed, but here, I’ll just fade them out.
The red Xs are our newly known blank spaces, and the blue cells show us cells we can fill, because we now know the endpoints for their groups.
I left the column with the 3 clue highlighted, because after placing the new Xs, we now also know the bottom of that group, so we’ll be able to fill in the cell at the top of the column.
After filling in all those cells, and then placing the Xs in the remaining spaces for columns we completed, it looks like the most helpful key to finish was the column with two 1s, highlighted here. Thanks to those Xs, we can go down the grid row by row and complete the remaining clues.
Starting at the top with the 6, we now know the start point, so just finish filling out that block, and place another X at the end.
Next down is the 2 with the beginning cell known toward the right side of the puzzle. We can fill that second cell out, and then close of the middle of the row with Xs.
Speaking of the middle, the next 2 down only has two open spaces in the middle of the grid. The last cell open in that row is only a single, so it couldn’t hold the required filled blocks for the clue.
Finally, the two bottom rows have a known endpoint, so we can fill the blank space before the known cells, and that will complete the puzzle.
The completed nonogram.
