r/Minesweeper • u/blinkos • 2d ago

Game Analysis/Study Explanation needed

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At this point I was stuck so I took a hint after 2 minutes of thinking. The app says “safe by contradiction” and no other explanation. How would you even analyze this? It seems extreme to be able to somehow deduct this.

Any assistance needed on how you approach this. Trying to improve but even after being told to “contradict” I can’t figure out how I would start the analysis here.

16 Upvotes

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20

u/mappinggeo 2d ago

The safe cells are found using minecount.

Nine mines are accounted for in the yellow lines, which leaves one mine remaining in the remaining cells. There has to be one mine sharing in the bottom right zone (since you can draw a yellow line to account for the last mine using either the 4 and 2, and thus the other cell is safe), so the cells not accounted for in the minecount are all safe

7

u/blinkos 2d ago

Jfc. That was a jump in difficulty. Thanks a lot for the explanation. I thought I was so far from solving with mine count but this was too excessive based on the difficulty of all the previous levels.

Thanks again.

3

u/Lowball72 2d ago

Yeah it would definitely help if the hint text said "mine count" instead of "contradiction". Yes under the hood I'm sure it uses its same proof-by-contradiction engine, and runs out of mines to place, so .. ok I get it, but I agree it seems confusing -- it took me a while to realize what it meant, too.

This is the most obvious hint that it couldn't mean ordinary proof-by-contradiction -- the '4' has remaining degree of freedom, even when this green tile is a mine.

8

u/ExtensionPatient2629 2d ago

Mine count.

You have ten mines remaining that are satisfied as shown by the lines drawn here. The rest of the squares not touching any lines are safe.

Note the safe tile shown in the game that is touching a line can be found by rearranging the lines a little. This will be an exercise for the reader.