Combinations Summary

Quick rundown of what the drawings below the explanations mean:

Light gray cells = “air” cells, or mines

Dark gray cells = covered a.k.a unknown cells

Yellow lines = cells connected form a region that contains one mine

Orange lines = cells connected form a region that contains two mines

Red lines = cells connected form a region that contains three mines

Blue lines = air lines. Is used to mark cells that are not part of the region, but where the initial line still goes trough

Maroon cells = Elimination Cell, reaches a contradiction if a mine

Green cells = Reverse Elimination Cell, reaches a contradiction if safe

Orange cells = Inverted Elimination Cell, reaches the opposite contradiction if a mine

Yellow cells = Inverted Reverse Elimination Cell, reaches the opposite contradiction if safe

Black cells = only when there are too many elimination cells, the non-elimination cells are marked instead.

Other terms:

Elimination cell = Cell that is considered a mine that creates a contradiction

Reverse Elimination cell = Cell that is considered safe, which creates a contradiction

Inverted Elimination cell = Cell that unlike the other elimination cells, is the opposite bound, lower bound vs upper bound or upper bound vs lower bound

“>” = Too many mines are needed, creating the contradiction

“<” = Not enough room to put down all of the mines, creating the contradiction, rarer.

Combo Box αβ

A structure found in a lot of combinations examples:

A few observations:

-The elimination cell seems to be in this box when the box is present, as seen in “Combinations #3”, there is no combo box, so the elimination cell is somewhere else

-The elimination cell seems to touch the triangle that is part of the structure, any combinations example that has this will be named “alpha”.

I feel like based on the fact that a good number of combinations patterns have these boxes, looking for these is a good idea. Keep in mind that these are not required for a combinations pattern, as seen in i.e. “Combinations #3”

< Combinations #8, this is somewhat similar to the box, but not completely. I will call this a broken box, type beta.

Factory Shape Γ

A shape found in quite a lot (mostly easier) combinations, examples (Comb. #3, Comb. #6):

A few observations:

-If there is a factory shape, there is not always a combination cell inside of it, but it still seems relevant.

-The base can vary, 3 mines (ex1) and 2 mines (ex2)

-There seems to be a yellow region next to it. This should be part of the shape.

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For now, I will name any combinations with the factory shape “gamma”, due to lack of sample

Other Types φ

φ = lacks sample, has some similarity to Γ