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Different Neighbours

Posted: Sat 19 Oct, 2019 7:50 am
by Puzzle_Maestro
Whenever I solve a different neighbours puzzle, I tend to painstakingly pencilmark numbers until I get somewhere. This normally allows me to solve the puzzle eventually, but it is not quick. Is there a trick (or multiple!) to solving this kind of puzzle more quickly?

Also, there is clearly a lot of potential for bifurcation, as there tends to be a lot of bi-value cells. However, normal bifurcation (writing out candidate in each cell) would take a lot of time and effort. Is there a quicker way to bifurcate?

Finally, on a video regarding the A.R.T method for solving sudoku (discovered by Sam Cappleman-Lynes, it seems!), someone commented that this method was applicable to suguru (capsules) and different neighbours. However, I have no idea where best to place the givens to make the puzzle as easy as possible, and I am not sure if this would save any time over solving the puzzle normally (as there is so much rearrangement needed at the end of the puzzle). Does anyone out there use this method to solve different neighbours?

Responses would be greatly appreciated!

Re: Different Neighbours

Posted: Sun 20 Oct, 2019 1:37 pm
by detuned
I find the quickest way to solve harder examples is just to take a guess and hope you get to a contradiction sooner rather than later. There are a few techniques you can use before you need to resort to that though. Notating where numbers go across two adjacent cells can propagate very quickly across the grid in pairs of cells for example

I think if you want to be more rigorous, then yes, you effectively have to do a colouring of the cells (for example by letters A,B,C etc) and then hope you get to a point where you can map A=1 B=2 etc

Re: Different Neighbours

Posted: Mon 21 Oct, 2019 12:43 am
by kiwijam
Yes, obviously finding points where 4 cells meet help you propagate information quickly.
Another thing that sometimes pops up is having a chain of cells where every 2nd cell must be a 4. If this chain loops back on itself then it must be even length, so you may be able to rule out options that would cause an odd-length loop.
Uniqueness pops up regularly too - in little dead-end regions, some values in the penultimate cell may leave two unresolvable options for the final cell.

But I feel slow at these generally, and it's not a bad idea to start in pen and then switch to pencil for an early guess.

Re: Different Neighbours

Posted: Thu 24 Oct, 2019 10:57 am
by Puzzle_Maestro
Thanks both!

I've never tried starting a puzzle in pen and then switching to pencil due to fear of making a mistake (which happens frequently when I am going for speed). However, I have thought about using, say, a 4H pencil (hard) and then switching to a 4B pencil (soft) for guessing. That way, when you erase your guess, you will only erase 4B markings, and 4H markings will still remain mostly intact (but can be erased if necessary).