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This was on the entrance exam at our local university last year.
I still can't figure out the answer... enter image description here

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Each number on the point is the sum of the squares of the numbers connecting to it.

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Any intuition about whether there's a pattern to the inner numbers? – Parthian Shot Mar 7 at 19:25
I doubt it. If anything, it seems to be made to be easy to figure out. Putting 5 or 6 next to 4 would give 41 or 52, neither of which is obviously a sum of squares. Although four of them being multiples of five might be an intentional red herring. – Lacklub Mar 7 at 19:30
@ParthianShot: (n+1) goes to n-th unfilled field clockwise – Erbureth Mar 8 at 13:35

$5^2 + 6^2 = 25+36$= $61$
Its just square and add

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The way I saw it was noticing that the bigger numbers in the "outer circle" seem to relate to the bigger number in the inner circle. Then I first noticed $5^2 + 1 = 26$, and seeing $4, 3$ and $25$ we have the famous pythagorean triple giving $4^2 + 3^2 = 5^2$ – Improve Mar 7 at 19:19
@Improve same case with me...coz I also saw the famous pythagorean triplet first...and later came to the conclusion.. :) – manshu Mar 7 at 19:22

Every number at the points is equal to the sum of the squares of the closest two numbers inside, so it's 25+36=61.

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