Minefield Puzzle V – Walkthrough

  1. A1 tells us that “No 3 safe squares or 3 mines form an L shape (of any rotation).”  Since A1 & B1 are both safe, this means that A2 and B2 must both be (M)ines, otherwise we would form an L-shape between either A1-B1-B2 or B1-A1-A2 .
  2. The same logic from step one will now apply to the A & B rows for all the columns.  For all A&B rows, safe & mine squares must alternate between the odd & even columns, respectively.  A3 & B3 must be (S)afe (to prevent L shapes, as described above), A4 & B4 must be (M)ines, and A5 & B5 must be (S)afe.
  3. B1 tells us “If B5 is safe, C5 contains a mine. ”  Since we know B5 is safe, that means C5 must be a (M)ine.
  4. We can now use the L-shape rule to complete the rest of row C.  C4 is (S)afe (preventing a B4-C4-C5 L-shape), and for similar reasons, C3 is a (M)ine, C2 is (S)afe, and C1 is a (M)ine.
  5. We now have only row D remaining.  If we consider D1 & D2, we know that they cannot both have the same value (since two mines would create an L-shape with C1, and two safes would create an L-shape with C2).  This logic will apply to the entire row – no two spaces can have consecutive instances of the same value (M or S) without creating an L-Shape with a value from the row above.  This means that the values must alternate – either M-S-M-S-M or S-M-S-M-S.  Since A5 tells us that “There are fewer mines than safe spots in this puzzle,” we know the pattern must be S-M-S-M-S – otherwise we would have 10 mines and 10 safe spaces, violating A5’s rule.  This means that D1 is (S)afe, D2 is a (M)ine, D3 is (S)afe, D4 is a (M)ine, and D5 is (S)afe.