10
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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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20
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61

Because

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

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  • $\begingroup$ Any intuition about whether there's a pattern to the inner numbers? $\endgroup$ – Parthian Shot Mar 7 '16 at 19:25
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    $\begingroup$ 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. $\endgroup$ – Lacklub Mar 7 '16 at 19:30
  • $\begingroup$ @ParthianShot: (n+1) goes to n-th unfilled field clockwise $\endgroup$ – Erbureth says Reinstate Monica Mar 8 '16 at 13:35
11
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$5^2 + 6^2 = 25+36$= $61$
Its just square and add

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    $\begingroup$ 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 $4^2 + 3^2 = 5^2$ $\endgroup$ – Improve Mar 7 '16 at 19:19
  • $\begingroup$ @Improve same case with me...coz I also saw the famous pythagorean triplet first...and later came to the conclusion.. :) $\endgroup$ – manshu Mar 7 '16 at 19:22
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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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