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Some days ago I noticed one simple task from the first point of view. It's from mathematical tournament for 11-12 years old. I don't remember exact description, but I'm sure the answer has to be an integer.

enter image description here

I found only the following dependency (for diagonal sectors): $\frac{51}{14}a - \frac{13}{7} = b$

So, my answer is $81 \frac{13}{14}$

Any ideas how to have an integer in the answer?

Finally I saw the solution of this task and it's absolutely stupid. I don't know how such badly described task can be used for math contest even for 12 years old children. There is nothing interesting to discuss. Initial image is updated.

user2700840
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    In theory, you can put whatever value $a \in \mathbb N$ and justify by saying that all values are solutions of the equation $$(x-a)(x-20)(x-6)(x-23)(x-71)=0$$ – NN2 Dec 05 '22 at 07:11
  • @JeanMarie it's just circle with 6 sectors. I think angles and other geometrical proportions don't matter (I drew it in Paint from memory) – user2700840 Dec 05 '22 at 10:10
  • @NN2 I don't think such answer is expected from 11-12 year old children :) – user2700840 Dec 05 '22 at 10:16
  • My question is stupid: evidently the intersection doesn't take place in the center of the circle ! – Jean Marie Dec 05 '22 at 10:28
  • I don't understand your computation. What do mean by "diagonal sectors" ? – Jean Marie Dec 05 '22 at 11:03
  • I have taken the liberty to modify your initial tag; "logic" tag refers to "mathematical logic" which is very different from 'logic" in "use your logic to solve a question". – Jean Marie Dec 05 '22 at 11:22
  • The more I work on your issue, the more I think some data is missing. – Jean Marie Dec 05 '22 at 12:24
  • @user2700840 - NN2 was trying to point out to you that you are on a fool's errand. It is a major weakness of "spot the pattern" questions that with a very limited sample size, there are multiple patterns that can be found, each of which gives a different answer. Without the full description of the original problem, this is such a "spot the pattern" question. It is pointless to attempt, as there is no reason to believe that any one pattern is the "correct" one. – Paul Sinclair Dec 06 '22 at 02:10
  • Could you give us the answer that you qualify as "absolutely stupid" ? I am interest because I have spend already hours on it ! – Jean Marie Dec 06 '22 at 20:37
  • I realize that my initial assumption that these numbers are areas is maybe wrong ? – Jean Marie Dec 06 '22 at 22:58
  • @JeanMarie On original image there were 4 sectors which are a bit smaller (very) than 2 others (with value 6 and 20 placed diagonally). But there was nothing is description about it (not about they are smaller/bigger, not about they are equal). So, dependency is easy, but anyway I don't like it at all. For smaller sectors: smaller sector value * 3 + 2. E.g. 23 * 3+2 = 71 – user2700840 Dec 07 '22 at 09:45
  • Thanks. I wouldn't have guessed ! – Jean Marie Dec 07 '22 at 09:54

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