What is Parity?

[SureLockHomes]

It seems to indicate that the solution to a hint involves the mine count, but I don't understand what deductions are being made. Could someone provide a clear definition of parity as a technique, or show an example of it being used?

Thanks

[GM Alexandria]

Parity means 'odd or even'. It mostly shows up in snake. When you have two portions of snake, they will always either need an odd or even number of mines to connect them. If they need an even number of mines, and you have an odd number left, then parity means you need to add an odd number of mines to the other end of one snake, for example.

[Perseus]

Originally posted by GM Alexandria:

Parity means 'odd or even'. It mostly shows up in snake. When you have two portions of snake, they will always either need an odd or even number of mines to connect them. If they need an even number of mines, and you have an odd number left, then parity means you need to add an odd number of mines to the other end of one snake, for example.

To add to this, you can most easily see tile parity on chessboard-colored levels, where tiles of the same color have the same parity.

For an example of using parity in Snake levels, imagine you know exactly where one of the ends of the snake is.
How many mines are there in total? An even number?
Then, you know that the other end of the snake cannot be on a tile of the same parity as the first.
Why? Because for the snake to "move" from a tile to another of the same parity, it always needs to "move" an even number of times, and the starting point is also a mine.
1 + [even number] = [odd number]
Odd numbers are obviously not even, so if the total number of mines is even, then the ends of the snake cannot both be on tiles of the same parity, because that would mean an odd number of mines.

[SureLockHomes]

Very interesting. Thanks for the explanations! Snake is quickly becoming my favorite variant so far.