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 Four Squared (Posted on 2006-10-26)
```        Grid A                    Grid B
A   B   C   D             A   B   C   D
+---+---+---+---+         +---+---+---+---+
1  |   |   |   |   |      1  |14 |23 |34 |14 |
+---+---+---+---+         +---+---+---+---+
2  |   |   |   |   |      2  |31 |42 |26 |26 |
+---+---+---+---+         +---+---+---+---+
3  |   |   |   |   |      3  |22 |24 |44 |29 |
+---+---+---+---+         +---+---+---+---+
4  |   |   |   |   |      4  |12 |32 |19 |16 |
+---+---+---+---+         +---+---+---+---+
```
The numbers 1 to 16 are to be placed in grid A, so that consecutive numbers are not adjacent in any direction, including diagonally. Nor do they appear in the same row, column or any diagonal.

The number in each cell of grid B is the sum of the horizontal and vertical neighbors of the corresponding cell in grid A.

NB. The letters and numbers around the edge of the grid serve no purpose for the solver. They are to be used for identifying cells in the solution.

 See The Solution Submitted by Josie Faulkner Rating: 4.4167 (12 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
 A trivial way to solve this | Comment 1 of 17
Looking at grid B, write 16 linear equations (such as B1+A2=14, A1+B2+C1=23, and so on) and solve the system.

Just in case, if there are many solutions, try fixing A1=1, and see where it leads; if that doesn't work, try A1=2, and then A1=3, and so on.
 Posted by Old Original Oskar! on 2006-10-26 14:18:36
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