# Fill the missing number puzzle

I have this puzzle that none of my colleagues (including me) can figure out and I can't sleep because of it :). Can someone please help:

Thank you.

• What does the hollow ellipse correspond to? – Laschet Jain Mar 11 '16 at 11:09
• "I can't sleep because of tit"... lol can't help you. – Daedric Mar 11 '16 at 11:16

My guess would be

the missing number is $3$

## Explanation

If we denote the four numbers by $a,b,c,d$, in clockwise order, starting with the lower left position (so that in the left picture $a=2$, $b=8$, $c=14$ and $d=9$), then these number satisfy the relation

$d*a-(b/a) = c~~~~$ Indeed, $9*2-(8/2)=14$ in the left picture.

In the right picture, the unknown $x=?$ then should satisfy $x*3-(15/3)=4$, which yields the answer $x=3$.

• Thank you very much, kind sir. But what is the purpose of the circle? – Radoslav.Ivanov Mar 11 '16 at 11:36
• @Radoslav.Ivanov: I have no idea about the purpose of the circle/ellipse. Also, my answer is just a guess; there might be better answers that also explain the ellipse. – Gamow Mar 11 '16 at 11:54
• Also can you explain the relation between the numbers, because as I understand it the equations c = da - b/a, so d = bc - b/a which is not 9... – Radoslav.Ivanov Mar 11 '16 at 12:17
• But the equation c=da-b/a yields d=(b+ac)/a^2. In the left picture this means 9=(8+2*14)/4, and in the right picture this means d=(15+3*4)/9=3. – Gamow Mar 11 '16 at 12:25
• With only 1 complete sample we could make many relations fit. Like a+b+c+d=33, which makes the answer 11. There's gotta be something something else, like the circle, that determines the right answer. – Kruga Mar 11 '16 at 13:49