How to solve Link-a-Pix puzzles

Overview

A link-a-pix puzzle consists of a partially filled grid of numbers, generally rectangular. The goal is to draw paths between numbers so that the number represented on either end of the path represents the number of squares in the path. Paths can turn multiple times, but can only consist of a series of horizontal and vertical segments (no diagonals). Squares can belong to at most one path. Black all squares in paths to create a picture.

Here is a sample unsolved link-a-pix grid and the solution (a camel with a sun in the background):


Fig. 1: Unsolved grid		Fig. 2: Solved grid

Link-a-pix are among the easier of the picture style of puzzle, and much of the advanced strategy consists of trial-and-error of drawing paths and seeing what gets blocked.

Strategy Summary

Basic Strategy

Black all 1s

Pair up 2s

Work with 3s and 4s

Work with larger numbers

Basic Strategy

Black all 1s.

All cells with 1 have to represent paths of one square, and therefore can be blacked.

Fig. 3: Black all 1s

Pair up 2s.

2s must always be paired with neighbors. In some situations, 2s can be paired with multiple neighbors, but there will always be a single way to pair them all up.

Fig. 4: Pair up all 2s

Work with 3s and 4s.

In general, it's easier to pair up smaller numbers first. This will also create blockades for paths with larger numbers. In this case, first consider the 3s. The red line indicates a path which connects two 3s, and is three squares long, but it goes through another path (a 5-5 path), and therefore isn't valid. The orange line indicates a path which connects two 3s and doesn't go through any other paths, but it's longer than three squares. The only way that the 3s can be connected according to the rules is shown in blue.

Fig. 5: Pairing up 3s

Now consider the four 4s that mark the corners of a square. The lower 4s could be connected, with the orange line, but that would mean that the upper 4s would have to be connected with the red line. This travels through the 5, and therefore is not allowed. Therefore, the 4s must be connected up and down, as shown with the blue lines.

Fig. 6: Pairing up 4s

Note that two 4s next to each other have to be connected by a line with two right angles. In both cases, there is only one way to draw that line that follows the rules.

Fig. 7: Neighboring 4s

Work with larger numbers.

All that's left in this puzzle is the pair of 5s, which can only be connected as shown below. This finishes the puzzle.

Fig. 8: Finishing up

Paths can get fairly complex about 5, though, folding in on themselves. Look for pairs of numbers that can only be connected by a straight line to cut off areas of the grid. Also, look for unique numbers; if there are only two 10s in an area of the grid, they have to be connected to each other. Finally, look for numbers that can't be matched by a path; for instance, if two 9s neighbor each other, there's no way to draw a line between them (only even numbers on the same path can be neighbors), so they must connect to two other 9s.

Conclusion

These strategies should be sufficient to solve most any link-a-pix puzzles you choose to tackle. As you solve more puzzles, you will begin to see other patterns that will simplify solving. All puzzles will have a unique solution which can be entirely determined by logic. Have fun!