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I'm playing minesweeper on a website that says you can win using pure deduction without guessing, and I am currently stuck in the top left corner of the map. It's a 30x16 grid with 170 mines and the rest of the grid is solved. Is this possible without guessing? Since there are 5 blocks on the top left corner that are not bound by any numbers they can be used to pick different possible outcomes for the remaining 9 mines that all work based off the scenarios I tried imagining.

One thing I concluded was that in order for the pair in the top to be solvable by deduction they either both have to be mines or both have to be clear. I'm not sure if that is 100% true.

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2 Answers 2

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Row 3, column 2 is safe because of the 4.

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  • $\begingroup$ Thanks! I didn't catch that one $\endgroup$
    – LDR
    Dec 4, 2020 at 1:27
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The assertion that you can win Minesweeper using pure deduction without guessing (guaranteed)... is false. This is obvious in the example given; there is simply no information about elements 6, 10 and 11 in the top row. (Theoretically, the website might have an algorithm that guarantees that each puzzle it gives is solveable... but if so, it is faulty.)

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    $\begingroup$ The website's algorithm is not necessarily faulty. The total number of mines is known, so it could well be that after the rest of the board is solved, all the remaining blanks must be mines. $\endgroup$ May 16 at 13:14
  • $\begingroup$ Sorry, downvoted. The existence of such an algorithm is not merely theoretical, see for example the version from Simon Tatham's collection. In that version too, you often run into situations like this one where in the end you can conclude that either all three cells contain a mine or none of them do. $\endgroup$
    – Oliphaunt
    May 16 at 18:05

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