Clarification/Follow-up by IQGuru on 08/06/06 8:55 am:
Hi there!

It should first be presumed that color has no bearing on the number value of each shape, any more than color would affect the addition of any other set of numbers. Then, the key to solving this problem is to notice that only 4 different numbers are used, and that the same number symbol appears atop the first column, and 3 more times in the second line, and once more as the last number in the third line. Similarly, there are other numbers that appear several times in various places. So, anytime a symbol is solved, merely place that same symbol in all of its other places...

So the numbers you are really looking for (and lettered in the order in which they can be found by substitution within the various lines and columns) really look like this:

A +B +D +C=16
A +A +A +B=23
C +D +C +A=18
B +C +D +C=13
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20:16:17:??

Thus, by trial and error, trying A=7, the solution number is 17 and the matrix is:

7 +2 +3 +4 = 16
7 +7 +7 +2 = 23
4 +3 +4 +7 = 18
2 +4 +3 +4 = 13
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20:16:17:17

Warm regards,
IQGuru

Clarification/Follow-up by henriyaz on 08/06/06 11:36 pm:
Thank you very much, my dear Guru ( Teacher)