Nonogos

If you like solving nonograms, then you've come to the right place! Nonogos is a puzzle game in which you solve nonograms, of which the puzzle grids can have any dimensions. That about sums it up!

Those who have not heard of nonograms may be asking themselves, "What is a nonogram?" The premise is similar to sudoku in that you fill out a grid with the help of numbers, but that's also where the similarities end. Each row and column of the grid has one or more numbers attached to them. These numbers tell you how many spaces of that line in the grid should be filled, with each number representing a group. The groups should be separated by at least one empty space between them. Your objective is to fill the grid using the numbers to essentially create pixel art.

Here we have a basic 3x3 nonogram. On the left, we can see the nonogram's initial state, an empty grid. To the right of it we have its solution. The grid has been filled using the numbers shown alongside the edges of each row and column. How does one go about solving a nonogram? Let me explain using the nonogram on the right with the highlighted areas.

The area highlighted in green, the encircled 3 on top, shows us a number. The number tells us how many squares should be filled in in order to solve the line it's connected to, whether a row or a column, Each number represents a group, meaning X number of filled squares should be connected with no emtpy squares in-between. As this number says 3, that means we should have 3 filled squares next to each other, and in this case it also means that the entire column should be filled. Why? Well, the sum of the column's numbers equals that of the nonogram grid's column height. As the grid is 3 squares tall, and our column should have 3 filled squares, we can determine that the entire column should be filled. Checking the sum of the total number of squares that should be filled is very useful.

For example, look at the yellow area that encapsulates two 1's on top, where we have two separate groups of 1 filled square each. The numbers being separated means that the two groups should not connect, that we need to have at least one empty square between each group. When thinking of a line's sum, think of this empty square as adding 1 to the sum. If we have this line with two 1's, think of it as 1 + 1 (+ 1) = 3. As the sum in this case equals to that of the line's length, we can deduce that the entire line can be solved. In essence, think of the space between two groups as a hidden group of at least 1 empty square,

The area highlighted in red that encapsulates the single 1 on top shows a column. Here we have a group that should only contain 1 filled square, and as it's also the only group we know that there should only be 1 filled square in the entire column. No more, no less. On its own it's impossible to know which square should be filled, and so we will only know which after we have filled in more of the nonogram's grid.

The area highlighted in blue that encapsulates the single 2 on the left side shows us a row. The 2 signifies that this row should have 2 filled squares that connect into a group. Where the 2 square are is a mystery until later, but what we can deduce from it is that the middle square can be filled, leaving only 2 possible locations for the other filled square to be. We can get that information from comparing the line's sum to that of the grid's dimensions. If the sum is over half of the total number of squares remaining, there is at least one square that can be filled. Using our current nonogram, we have to fill in 2 squares in a row that's 3 squares wide, and as 2 is more than half of 3 (1.5) we know that we can fill in at least one square in the middle.

That should be enough information to get you going! Now that you know how to solve nonogram, give Nonogos a go, no?