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3 boxes
The numbers in all the three groups follow the same mathematical pattern.
Can you work it out?

Note : The 4 numbers in a square form a single group, and the answer is a positive integer.

Please try first without the hints.

Hint 1: You have to work on equations involving addition.
Hint 2: You should calculate the powers of each number.

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  • $\begingroup$ "there are several possible, and valid, solutions" This means the question is too broad in my opinion. If you add enough hints so there is only a single valid solution this question might be good enough $\endgroup$ – Ivo Beckers Sep 29 '15 at 8:50
  • $\begingroup$ @IvoBeckers If someone uses hints, then there is exactly one mathematically correct solution. I have found 2 correct solutions till now. $\endgroup$ – ABcDexter Sep 29 '15 at 9:00
  • $\begingroup$ @IvoBeckers, Ok should I narrow it down the question to only one solution ? That would be killing the creativity and fun :-/ $\endgroup$ – ABcDexter Sep 29 '15 at 9:05
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    $\begingroup$ There is a difference between a hint which will usually guide people more easily to the correct solution and a condition or restraint that reduces the number of valid solutions. The way you have phrased this question, there could be a number of valid solutions. If you wish to add constraints then they need to be part of the main question, not hidden in spoiler tags. $\endgroup$ – Gordon K Sep 29 '15 at 12:53
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    $\begingroup$ Perhaps you should give two or more examples instead of only one example. The current example has square(6)+square(8)=square(1+9), that is, square-of-upper-left-number plus square-of-lower-right-number equals square of (upper-right-number plus lower-left-number). And I can come up with tons of other potential solutions. $\endgroup$ – Gamow Sep 29 '15 at 16:33
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The answer is:

87

How to find it:

Label the contents of the square A / B / C / D, with A upper left, B upper right, C lower left and D lower right.

Based on these names for the spots, we find:

(A³ + D³) = (C³-B³) for all examples.

We now know:

x³ + 25³ = 90³ - 38³, or x³ = 658503, which solves for x = 87.

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