incredibly simple puzzle concept: draw lines in a grid that connect each pair of numbers. While the rules are easy to understand, the puzzles can be difficult to solve without some experience. And while I’ve wanted to construct more Numberlink puzzles for awhile, Numberlink (and related path puzzles) are the single type I am least confident of constructing without errors. Nothing else comes close.

The challenge of constructing a Numberlink puzzle is not in placing a set of paths into a grid to get an answer (although doing this with challenging paths and theme elements like symmetry or no numbers on the border as below can be difficult). The challenge is ensuring that there is exactly one solution: your intended solution. Among logic puzzle solvers, having multiple solutions to a challenge is one of the biggest no-nos.

Unlike something like a sudoku puzzle which tends to solve through repeated application of simple heuristics, Numberlink puzzles rarely allow such deductions and instead solve based on a combination of intuition and meta-logic. I have a few notions from topology/knot theory that can help at times, certainly on the easiest grids, but there’s still no easy way (that I’m aware of) to check a puzzle has a unique solution by logic, and no easy way to code an efficient solver either. But brute-force computational search certainly works at these sizes, which is what I’m using now to give me some confidence that my hand-crafted grid this week only has one answer. This puzzle should take much less time to solve than it took my PC to check; I hope you find it enjoyable.

Rules: Connect each pair of numbers with a continuous line that only passes vertically or horizontally between squares. Lines cannot pass through the same square twice, and no two lines can cross each other or occupy the same square.

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Authors: Thomas Snyder

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