Maths: One for the Weekend

[nareluin]

Nareluin will donate 200 tokens to the first person that posts the correct solution to the following puzzle:

This is a puzzle I read a long time ago. You have to fill the box (drawn below) with consecutive numbers from 1 to 16.

 ___ ___ ___ ___
|A  |B  |C  |D  |
|___|___|___|___|
|E  |F  |G  |H  |
|___|___|___|___|
|I  |J  |K  |L  |
|___|___|___|___|
|M  |N  |O  |P  |
|___|___|___|___|

You cannot repeat any number, and you cannot leave an empty cell. The sum of the numbers in cells specified below, must return the number "34"

ROWS:
A+B+C+D=34
E+F+G+H=34
I+J+K+L=34
M+N+O+P=34

COLUMNS:
A+E+I+M=34
B+F+J+N=34
C+G+K+O=34
D+H+L+P=34

SQUARES:
A+B+E+F=34
C+D+G+H=34
E+F+I+J=34
G+H+K+L=34
I+J+M+N=34
K+L+O+P=34

DIAGONAL:
M+J+G+D=34

It looks complicated, but it just takes some patience!


By the way... On the original puzzle I read once, I thought there had to be a second diagonal (A+F+K+P) that returned 34. I remember I spent days trying to solve that one single result. I finally gave up, thinking I might have added an instruction that was never there (I didn't have them at hand to check them out again). If any of you would like to try it out, and finds a solution, I would be sooooo thankful =)

[Benny]

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

In this square:
- the sum of any row is 34
- the sum of any column is 34
- the sum of the 4 corners of any square is 34 (length 2, 3 and 4)
- the sum of the 2 major diagonals is 34
- the sum of any wrapped diagonal of length 4 is 34 (e.g. 12 + 2 + 5 + 15)

You can create 3 more like this by rotating it 90, 180 or 270 degrees!

[nareluin]

Well, this doesn't need a confirmation. I thought you'd come with an answer in no time. Enjoy your tokens! =)