User:Raisins/Groups of Cells

I'm going to talk about deduction in very a general way. This encompasses the simple patterns, but extends to almost any situation beyond counting the mines around a single cell.

A method

1. Pick a value cell to solve around
2. Count the remaining hidden cells next to it
3. Check other values that are next to those hidden cells
4. Use them to divide the hidden cells into groups
5. Account for all the remaining monsters, and hopefully:
   1. You run out of missing monsters: the remaining groups are SAFE
   2. You run out of groups: the remaining groups are ALL MONSTERS

Examples

1-2

Maybe you know the basic 1-2 pattern:

1-2 Pattern

Let's dissect this as groups of cells.

Hidden Cells

We have a we would like to solve. This has three nearby hidden cells:

Total monsters: 2
Hidden cells: 3

Groups

We have one other piece of information about these cells. There is a next to two of them. Separate the hidden cells into two groups we have different information about:

• Two cells next to the
• The leftover cell

Group A: Two cells next to the

Group B: The other cell

Count the monsters

Total monsters: 2
Group A: 1 monster
Group B: ?

There are 2 total monsters. We know the first group has one monster. Therefore the only remaining cell in group B must be a monster.

Result

Flag the extra cell.

4 with a 2

Hidden Cells

We have a we would like to solve. It has five nearby hidden cells.

Total monsters: 4
Hidden cells: 5

Groups

There is a next to three of these hidden cells. This is one group. Then there are two leftover cells.

• Three cells next to the
• First other cell
• Second other cell

Group A: Three cells next to the

Group B: Leftover cell

Group C: Leftover cell

Count the monsters

Total monsters: 4
Group A: 2 monsters
Group B: ?
Group C: ?

Four total monsters, three groups. Two in the first group according to the , therefore both remaining cells in groups B and C must be monsters.

Result

Flag the extra cells.

3 next to stuff

Hidden Cells

We have a we would like to solve. It has five nearby hidden cells and one nearby flag.

Total monsters: 3
Hidden cells: 5
Flags: 1

Groups

There is a nearby and , each next to a pair of the hidden cells around our .

Make four groups:

• Two cells next to the
• Two cells next to the
• The flag
• One final cell we know nothing about

Group A: Two cells next to the

Group B: Two cells next to the

Group C: The flag

Group D: The leftover cell

Count the monsters

Total monsters: 3
Group A: 1 monster
Group B: 1 monster
Group C: 1 mosnter
Group D: ?

Three total monsters. Group A has one monster from the . The is next to the flag, so Group B also has one monster. Group C is the flag, so obviously one monster. That is all three outstanding monsters, one each in the first three groups. Therefore the remaining cell in D is not a monster.

Result

Open the extra cell.

4 and then 1

Hidden Cells

We have a we would like to solve. It has five nearby hidden cells.

Total monsters: 4
Hidden cells: 5

Groups

There is a next to a pair of the hidden cells around our .

Make two groups:

• Two cells next to the
• The other 3 cells

Group A: Two cells next to the

Group B: The other 3 cells

Count the monsters

Total monsters: 4
Group A: 1 monster
Group B: ?

Four total monsters. Group A has at most one monster from the . There are three monsters left to fit and only three cells in group B. Therefore all of group B are monsters.

First result

Flag group B.

Reuse groups

Pivot to solving around the . Look at group A again.

Group A: Two cells next to the

We already knew group A had at most one monster, but now we can see it must have a monster to satisfy the . So if we consider these other cells around the

Group B2: Three other cells next to the

Count the monsters

Total monsters: 1
Group A: 1 monster
Group B2: ?

One total monsters. Group A has one monster from the . There are no monsters left. Therefore all of group B2 are safe.

Final result

Open the other cells.