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A friend posted this an hour ago and it kept me busy since. Anybody has a clue what the missing number is? I understand multiple outcomes are possible but i cannot find any. There is also a possibility he is joking with me, he sent a picture with this question on a sheet of paper. An explanation on how you found it would be neat.

$$12/84/ \_\_\_ /15626$$

miracle173
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Madmenyo
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    There's a unique quadratic function whose graph passes through the points $(1,12)$, $(2,84)$, and $(4,15626)$. It also passes through the point $(3,15866/3)$. Did you try asking your friend if he is joking with you? – Jonas Meyer Aug 15 '14 at 07:04
  • @JonasMeyer I asked him if it is solvable. – Madmenyo Aug 15 '14 at 07:07
  • I cant possibly add more info and it is a mathematical problem... So why the downvote? – Madmenyo Aug 15 '14 at 07:08
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    I am not sure it is a mathematical problem. Finding patterns in partial sequences of numbers can be part of mathematics, but isn't necessarily mathematics. Here there is no mathematical context. (By the way, http://oeis.org is a great place to check when there is reason to believe you have a start to a sequence that might be known. I don't expect it to help in this case.) – Jonas Meyer Aug 15 '14 at 07:11

2 Answers2

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A suggestion : \begin{array}{cc} 2^3+4&12\\ 3^4+3&84\\ 4^5+2&1026\\ 5^6+1&15626\\ \end{array}

Raymond Manzoni
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There are literally an infinite number of patterns that can be made out of this one:

If the third number is 1 the pattern can be demonstrated by

$$y(x) = \frac{15686}{6}x^3 - 8009x^2 + \frac{32623}{6}x + 12$$

If the third number is instead 2 the pattern can still be locked in by

$$ y(x) = \frac{7930}{3}x^3 - 8007x^2 + \frac{16307}{3}x + 12$$

and I can endlessly change the value of the third number and still prove there is a pattern.

Did your friend give any additional information to the type of pattern he/she wanted? Otherwise you can just mess with him/her and give both of these as valid answers

Sidharth Ghoshal
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