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.