Numberlink 20×9 easy puzzle

Over the past few years I’ve made at least one example of pretty much every reasonably popular Japanese number puzzle, but with one notable exception: Number Link.  In this puzzle the aim is to draw lines connecting squares with identical values in, but without these lines crossing over or visiting any square more than once.  The lines can also only travel horizontally or vertically, not diagonally.

In a completed Number Link puzzle, the lines will be placed such that every square is used – and that solution is guaranteed to be the unique solution too.  The rules are not, however, always stated that strongly.  In fact the most common form of the rules simply states that you must connect all sets of numbers, with an implied assumption that there is a unique solution, and furthermore again only an implication that that solution uses every square.  But in terms of solving the puzzles in practice, it’s fair to assume that:

  • There is a unique solution, and that unique solution happens to use every square

This assumption means that whilst solving a puzzle you can make various deductions about how lines can and cannot go based on noting what would make a puzzle non-unique, or not use every square.  Once you discard these assumptions (as you need to do when creating the puzzle, since you can’t assume uniqueness without proving it!) it’s typically much harder.

It stands to reason that as puzzles get larger that they can get much trickier, but that isn’t always the case: today’s first example puzzle, whilst quite large at 20×9, is actually really easy, as you’ll probably find out when you try solving it! :)