# Filling in an 8x8 minesweeper grid with mines (Day 7: Double Mines)

Note: This uses anti, single, double, and triple mines

Yes, I realize that when I uploaded Day 6, I mentioned in the disclaimer that I planned for this to be released tomorrow, along with Day 8, however the reason I'm uploading Day 7 right now is so I actually have some time to work on Day 8 since Day 6 ended up taking less time than I thought it would to get out on P.SE

Now, you might be thinking, "Hasn't there already been an introduction day?" or "Isn't the title a contradiction of what types of mines are used?" Well, the answers to the questions are respectively yes and no. Now here's the thing:

# Why isn't the title a contradiction of what mines are used?

Say we have this layout: (no, it doesn't matter if the example grids can be filled out without contradictions as long as I can get my overall point across. For example, with example 1, just assume there's another row above the 3 if you're annoyed with that.)

3
2
2
2 2 1
2 3 3 3 2

We know that there must be a mine at R3C4, however today, this implies automatically that there also must be a mine at R3C3 (hence the title "double mines") and at R2C4. However, take a look at this next grid:

3
1
1
2 2 1
2 3 3 3 2

We know that there must be a mine at R3C4 and at R3C3. However, because of the 1 at R2C5 and R3C5, a mine cannot go in R2C4. However, this is still a valid grid setup. Why? This is because we don't necessarily need a mine there. We already have the 2 mines at R3C3 and R3C4 connecting each other orthogonally. Now, you might be confused about why having the mines (in the first example) at R3C3, R3C4, and R4C4 isn't a contradiction of the rules. The reason this is because we have the mines at R3C3 and R3C4 connecting each other orthogonally, and then we have the mines at R3C4 and R4C4 that connect each other orthogonally.

## One more example

Take a look at this grid:

3 3
12 3 3
6 3
3 3 3
0 0 3 3 3

Now ignoring the contradictions in C4 and C5, we know that there must be triple mines at R1C1, R1C2, R2C1, and R3C1. If this confuses you, the reason we can have this be a valid grid setup is because we have that the mines in R1C2 and R1C2 & R2C1 and R3C1 are both connecting each other orthogonally. We just need 2 mines orthogonally connecting each other everywhere for it to be a valid grid setup.

One more thing to mention is that it really does not matter what the value of the mine is, if they connect to each other orthogonally, then it's valid.

Bonus puzzle (not required for the green checkmark, more just to deepen your understanding of this gimmick): Why would this not be a valid grid setup?

(Hint: There are 5 missing numbers in this grid with 8 anti-mines: -1x2, -2x1, -3x2)

(Hint 2: There's only one contradiction because having mines at say R1C1, R1C2, and R1C3 is valid, along with R1C1, R2C1, and R1C2. However, it would not be valid to have mines at R1C1 and R2C2 since they don't connect each other orthogonally.)

-2
-2 -2
-2
-1 -1 -2
-1 -1 -1 -1 -1

# The puzzle

1
4 7 14
7
-7 5 8
1
0 -3 4
6
1 5 2 1 3 3

There are:

14 anti-mines

4 single mines

3 double mines

11 triple mines

Missing numbers:

1x2

2x1

3x1

4x0

5x2

6x1

7x1

8x2

9x0

10x0

11x0

12x1

13x0

14x0

Hint:

R1C8 is a "clearing" - there isn't a number or mine there. The only reason this is is because there was a stray single mine there that would have made the puzzle invalid and I really didn't want to remove any of the numbers because then I would have to do a recount of the numbers that were affected.

• wait I just realized that this means that I need to fix the count for the single mines quick since I removed the stray mine after I did the count so that breaks the single mine count. Edit: actually it seems that either way I'll have to increase the single mine count since there are columns that I accounted for the other mines except for the single mines Commented Oct 30, 2023 at 20:48
• So is the restriction simply "no mine (of any type) can be orthogonally isolated from other mines (of any type)"? Commented Oct 30, 2023 at 21:04
• @BenjaminWang Basically, yes Commented Oct 30, 2023 at 21:06