Minesweeper Logic
In this Minesweeper game, we can determine with certainty that one of the untouched squares does not have a bomb. Which one is it? Enter the number that corresponds to the correct square in the diagram below.
Notes: (in case you're not familiar with Minesweeper or need a refresher)
- The number on a white square represents the number of bombs adjacent to that square (including diagonally). White squares do not have a bomb on them.
- A red flag indicates a square where we already know there is a bomb.
- Blue squares without a flag are "untouched". We are not given whether they have a bomb or not.
The answer is 10.
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1 solution
The blue 4 above the 6 or 7 has 3 bombs already; to fulfill the bomb count, 6 or 7 must have a bomb. This is the 3rd bomb for the blue 4 underneath the 6 and 7.
Now consider the pair of green 2s at the bottom. Each is next to a bomb already; either 15 or 16 has the 2nd bomb.
If we try 16 as a bomb, then 14 is free and 13 is a bomb (the nearby red 3 has 1 bomb to the left from the 2). This means 10 has to be free since the blue 4 has 4 bombs then.
If we try the other choice of 15 as the bomb, then 16 is free and 14 has a bomb. But then again the green 4 has 4 bombs.
In both cases 10 is free, hence no matter the circumstance 10 has to be free!