How to Solve Paint by Pairs Puzzles

Paint by Pairs is one of many names for a puzzle that was originally called Number Net when it was first published in the Japanese puzzle magazine Byakuya Shobo. It was popularized worldwide after Conceptis developed an algorithm to generate their Link-a-Pix puzzles.

Paint by Pairs is similar to Arukone, in that you will be connecting identical numbers, although here, there will usually be more than one pair of each different number, and the number 1 will always be a “pair” by itself.

You want to join pairs of identical numbers with a path. This path must contain a total number of cells equal to the numbers you’re joining, including those numbered cells. For example, a path that connects a pair of 5s will contain both 5s, and three empty cells between them. A 1, of course, is a complete path all by itself.

Paths will only travel orthogonally, although they may change direction. No path may cross another, or contain any numbers not part of the pair being joined. After drawing the lines, you can shade in all cells containing a path line to see a hidden picture.

Typically, you want to start with the easiest pairs. As stated before, a 1 is a pair all by itself, so any 1s on the grid can simply be filled in.

Next, look for 2s, as a pair will always be directly adjacent to each other. Occasionally, you may see a cluster of many 2s, but you can usually work out which pairs go together pretty easily.

Often, starting with the low number pairs and working your way up to the higher numbers helps define where those long paths can go.

Pairs of 3s are also fairly simple, since there’s only one empty cell between the numbers. They will basically only be in one of two path configurations.

Either a straight line, like most of the sets in this puzzle, or diagonally adjacent to each other, as seen with the pair I’ve highlighted in yellow.

Many times with a diagonal set, you will have to wait until later in your solving process to know which way the path will go, but in this case, the 4 blocks the other direction, so we know it had to go left and down.

For the next step up, there are many clusters of 4s, and so lots of ambiguous possible paths.

What you will want to do is start looking for numbers that are pretty isolated from matching numbers. That will limit the possible matches within range, and can help you create some paths that will narrow down your options later on.

Here, the pair of 4s at the bottom pretty obviously go together. The pink 4 is near to the yellow one, but that would be a five-cell path, so it must pair with the 4 that is directly to its left.

The blue 4 is too close to the one diagonally adjacent, and it can only reach the 4 that is straight to the left.

That leaves the yellow 4, which is too far away from all but a single 4. Can you spot it?

Note that while I’m filling in the squares as we go along, you will usually want to just draw the paths when working with pencil and paper – much easier to erase if you find out a path doesn’t work.

We’ve isolated a couple more 4s, so we can mark those paths. Now let’s look over on the right.

The yellow 4 is within range of both the pink and orange 4s. However, if it were to be paired with the orange 4, both the pink and blue 4s would be isolated, and they don’t have a valid path to each other.

Therefore, our pairs here must be yellow & pink, and orange & blue.

We can now match up our final pair of 4s. Over on the right, the 7s have exactly 5 cells between them in a vertical line, so that’s also an easy match. Be careful with longer lines, though – sometimes they will zig-zag between two numbers that are fairly close together.

Next, we have an isolated 5 that looks like it can only reach the 5 in the middle of the group on the right, because to reach either of the others would require a total of seven cells.

That leaves only the 5 at the top and bottom of that group, so they must match together. After drawing the line we just covered in the last paragraph, their path must use the three empty cells to the right.