Here is another solution:
4  10  9   3
11  8  7   14
15  5  6   12
1  13  16  2
Joseph E Cooper
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If I understand the puzzle correctly, you need to place the numbers 1 to 
16 in a 4x4 grid such that no number is the sum of any of the up to 
eight surrounding numbers.   There are lots of solutions to this 
problem.  For the case where you start with 1 in the corner, I found 
124728 unique solutions after removing reflections and rotations.  The 
example with 1 in a corner which puts the lowest number in the lowest 
square when numbered left to right, top to bottom is:

   1  2  3  4
  11  7  8  9
  13 14 10 12
   5 16 15  6

The example with the fewest number of numbers not in their original 
places is:

   1  2  3  4
  14  7  8 13
   9 10 11 12
   5  6 15 16

This example has 12 of 16 numbers in their original position.

Another interesting example is the following:

   1 11  9 13
  14  5  8  7
  16 12  2  4
   3  6 15 10

This example has a unique property among any of the entries with 1 at 
the corner.  Can you see what the property is?

Kirk Bresniker
---------------------------------------------
This seems to work.  No idea if there are non-trivial other solutions!

David Fry
1	9	11	3
13	5	7	12
10	6	8	14
2	15	16	4
--------------------------------------------------------
HERE IS MY SOLUTION:

3      11     10     2
13     7      6      9
15     5      8      16
1      12     14     4

Joey Flowey
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(Ref, my recent puzzle) Sorry, correct solution is a follows:

7    5   12   3
11  1    2   13
15  8    4   14
10  16   9     6

Best wishes,

Bernardo Recamán
Bogotá, Colombia