Toroidal Number Link
Toroidal Number link 8×8 puzzle
Number Link at sizes up to around 10×10 may not necessarily be hugely challenging for everyone, but I bet you now that this puzzle certainly will be! Despite being only 8×8 it is really very difficult indeed. Or perhaps that’s just me – I’d love to hear that someone finds it easy, but I’m not expecting anyone to!
The rules of this puzzle are, however, very simple:
- Connect each pair of identical numbers with a single line
- Lines can travel horizontally or vertically between squares
- Only one line can enter any square (this means lines cannot cross or overlap in any way)
- Your lines may wrap around from one side of the puzzle to the other, so for example if you travel off the right-hand end of a row then your line will continue on in the left-most square of that row
There is a unique solution to this puzzle, and it uses every square. However, the solution is unique even without the constraint that it uses every square.
If you’ve played toroidal sudoku then you’ll hopefully understand how the wrap around works – when you go off the top of a column you come back on the bottom, and similarly (as stated above) for rows. If the basic rules of Number link itself confuse you, take a look back at a post a few days ago for an example.
And good luck – I think you’ll need it! 
Comments are closed.
about 15 years ago
I hope you realize that my ho-hum for these types of puzzles was not from the easiness but that I don’t know how to explain the logic of how to do them.
Tried figuring it out but felt as if I was guessing most of the time. So my question is, what are some logic rules to get going? With the other ones the strategy is to start from the corners and sides and work inwards. So without the walls, where is the logic to start (the 4s or 2s)?
The really good thing about this hard puzzle is it caused me to forget about it and complete some tasks this weekend that really needed to get done.
I’d probably like these puzzles more if I had more methods of how to do them.
about 15 years ago
The thing about Number link, which is why plenty of people don’t like it at all, is that there are very few hard and fast rules. It’s more about a ‘feeling’ as to how it goes – or in other words, essentially “informed guessing” born of experience!
The edges are obviously a great help in a normal puzzle, and you can massively prune the search space by considering non-uniqueness as you extend lines. For example in this puzzle I found almost any moves I made soon proved that I had clearly made any potential solution non-unique, since of course lines cannot ever ‘touch themselves’ in an adjacent square and still be part of a unique solution. Therefore it’s also the case that any empty space between lines/clues which would require a line to bend back on itself or ‘touch itself’ to fill it must also be part of a non-unique solution, and so the lines that created that space must be wrong too.
In regular puzzles you can also start by considering numbers with both pairs close to the edges, since these may well simply go around the edge in some way. Looking for likely crossing/non-crossing pairs also helps.
But most of that breaks down in this toroidal puzzle. Essentially I think it requires a trial+error approach which can be followed reasonably quickly only by applying a keen eye to what must cause non-uniqueness!
about 15 years ago
SPOILER:
After a break over the weekend I tried the puzzle again, and solved it in a couple of minutes. I chose to start with the 6 at the bottom-left and try connecting them directly, since they were close. Then I was forced to extend the 1, so chose the quickest path for that too, wrapping off the bottom beneath the 7. From there I pushed the 7 down and round via 3 corners to meet up, and then the 5 is forced. From there there are only a couple of choices, one of which finishes the puzzle successfully.