The Mine Puzzle


A four by four checkerboard has been "mined". Each cell contains either no mine, or just one mine. The mines were placed in such a way that the total number of mines directly neighboring, or in, each cell, is odd. Here, a direct neighbor is a cell that is one cell north south, east or west.

For convenience, label the checkerboard with letters:

         A | B | C | D
        ---+---+---+---
         E | F | G | H
        ---+---+---+---
         I | J | K | L
        ---+---+---+---
         M | N | O | P
      
Here's one example of how mines might be (incorrectly) laid:
         1 | 0 | 1 | 0
        ---+---+---+---
         0 | 1 | 0 | 0
        ---+---+---+---
         1 | 0 | 1 | 1
        ---+---+---+---
         0 | 1 | 1 | 0
      
This particular arrangement won't work, since, for example, Cell A has 2 mines in its neighborhood.

Can you find an arrangement of mines that satisfies these rules? When Will Shortz presented this problem on National Public Radio's Weekend Edition, he didn't provide a solution, saying "Just think about it".

I give up, let me see the solution.


Last revised on 05 January 1999.