# Hey, This is a 100th Puzzle of Mine!

Yep, this is my 100th puzzle here in PSE~
I'm really having a wonderful time here, thank you so much guys! ><
I planned to write a harder and bigger one, but it turned out I was too lazy to do that..
So anyway, this is Minesweeper (Mine Clones)!

Rules:

• Put exactly 100 mines in the empty cells such that each digit denotes the number of mines in its 8-neighboring cells.
• In addition, there are 32 regions here separated by bold lines. The regions are actually making up 16 pairs. It's also your job to determine the pairing.
• The two regions in a pair must have the same shapes and the mines in it are located in the exact same positions. However, the digits are not required to be the same. No rotation or reflection is allowed.
• The grey colors are just for cosmetics.
• Are the cells on the top right corner included? I would assume it is, but just want to confirm. Commented Jun 3, 2020 at 10:47
• @justhalf Yes, the TH part is included. Commented Jun 3, 2020 at 11:09
• Ah, so that's TH, didn't see that before. Commented Jun 3, 2020 at 11:15

## 1 Answer

(Write-up complete) Lovely (and tricky!) puzzle athin, and congratulations on your 100! The final solved grid looks like this (with paired regions coloured the same and mines represented by black squares):

Step-by-step solving process:

Step 1:

First, shade out all of the spaces we know cannot be mines due to the presence of a number or being adjacent to a '0'. Use a beautiful beige colour (courtesy of MS Paint):

Step 2:

Now focus on the 4 rectangles of height 9. If we consider the main grid (ignoring the part above the instructions) to comprise 9 columns of 3-squares width, then the 9-rectangle in column 3 cannot pair with the one in column 7 (since the '1' halfway up the column 7 9-rectangle cannot be satisfied). Similarly, the 9-rectangle in column 3 cannot be paired with the 9-rectangle in column 1, else the '4' in column 1 will only have 2 potential spaces for mines around it. Thus column 3 must pair with column 5 and column 1 with column 7. Re-colour accordingly and place mines where required:

Step 3:

By considering the '4' in the (now) light green rectangle in column 1 with the '1' halfway up its partner in column 7, we know that exactly 1 of the 2 cells to the 'south-west' of the 4 must be a mine. Similarly, by considering the nearby 1 in column 8, we know that exactly 1 of the spaces to the 'east' of the 4 must be another mine, which means that both spaces to the 'north' of the 4 contain mines. This then permits a few more deductions locally and pinpoints the position of another mine in the light green rectangles:

Step 4:

Consider now the 4 rectangles of height 6. The one in column 7 cannot be paired with the one in column 4, else its '1' cannot be satisfied. Likewise it cannot be paired with the one in column 3, else it blocks off the '1' that forms part of the '100' in neighbouring column 4. Thus it must partner the 6-rectangle in column 2, while those in columns 3 and 4 pair up. Re-colour and follow through other deductions as required:

Step 5:

Consider now the 4 rectangles of height 12. The one in column 4 has a mine in the top-left corner. This means it must pair with the one in column 6, since those in columns 8 and 9 have numbers in that space (and thus cannot have a mine there). Re-colour and follow through other deductions as required:

Step 6:

Now consider the 4 L-shapes. The one in the bottom-right corner of the grid has mines in its two 'north-west' corners. This forces it to pair with the L-shape straddling columns 5 and 6, since the other 2 already have one of these corners shaded beige as safe spaces. Re-colour and follow through other deductions as required:

Step 7:

Next turn your attention to the lower 3x3 square in column 5. We already know the identities of 8 of its 9 squares, and we can identify its partner by ruling out 4 of the other 5 similar shapes for incompatibilities:
- The boxes in columns 1 and 8 cannot have a mine in their bottom-left square;
- The higher box in column 5 would be left with only 1 possible space for a mine, but 2 are required;
- The box in column 3 would block off the adjacent '1' in column 4 with no legal spaces for its mines.

Thus this box must pair with the one in column 7. This also leads to some deductions in the light-blue L-shapes:

Step 8:

Now the 3x3 box in column 1 must pair with the higher box in column 5 (it is incompatible with the box in column 8 and would result in blocking off the '1' near the base of column 4 if paired with the box in column 3). Re-colour and follow through other deductions as required, including several in regions of other colours:

Step 9:

Now pair up and re-colour the remaining two 3x3 boxes, and follow through the ensuing deductions across other regions:

Step 10:

At this point, count up the mines we have already placed and realise we have already accounted for 72 of the 100 - we need to place 28 more. It doesn't look like there are that many blank spaces left at this point, so let's count those up too... Well, wouldn't you know it - 28 of those as well! Fill all the remaining spaces with a black mine and the solution is complete!

• Great answer! Nicely thought out Commented Jun 3, 2020 at 15:27
• A really great answer, very well done! And surprise, have another +100 bounty (tomorrow, after it's eligible to set one tho)! ^^ Commented Jun 3, 2020 at 22:52
• @athin Oh, that is a surprise! Well, thank you very much for all the many interesting and challenging puzzles you set. You're a quality contributor and we're privileged to have you! :)
– Stiv
Commented Jun 4, 2020 at 5:58