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puzzle

1 set contains: 3, 2, 1

2nd set: 6, 6, 7

3rd set: 10, 9, ?

What is ?

Choose from: 7, 8, 11, 12, 13

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  • $\begingroup$ You mentioned an image, so that brings the concern that we are missing some visual clues. Are the sets arranged in a specific way? Or are they just straight lines? The visual aspect may be key to understanding the question. $\endgroup$ – ChronoD May 5 '16 at 17:10
  • $\begingroup$ May be its 13. There are two sort of z shapes. One reversed, facing each other. The sum of each would be equal if ? is 13 $\endgroup$ – user1849962 May 5 '16 at 17:23
  • $\begingroup$ Awesome. Seems like you're all good to go with your first post. Welcome to the Puzzling Stack Exchange! :) $\endgroup$ – ChronoD May 5 '16 at 17:26
  • $\begingroup$ Although that solution doesn't seem completely satisfactory $\endgroup$ – user1849962 May 5 '16 at 17:26
  • $\begingroup$ I just wanted to put some information from comments that were attached to a deleted answer. OP has confirmed (in a deleted answer) that the top right circle has a 6, 6, and 7. - Despite one of the numbers appearing blurred, the top right number IS NOT a 5. OP has confirmed (in comment below) that all the circles are the same size, although the numbers inside the circle may not be. The 3 in the top left and the rightmost 6 in the top right appear larger. $\endgroup$ – ChronoD May 5 '16 at 17:54
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Perhaps it is

11

Reason being

if you take the sum of each circle you get 6, 19, and 19 + ?. If you add them together in pairs, you get 25, 38 + ?, and 25 + ?. 25 is a perfect square. If ? = 11, then you get 25, 36, and 49 for the sums, all perfect squares (and 5, 6, 7 which is in order and slightly comforting).

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  • $\begingroup$ Seems plausible $\endgroup$ – user1849962 May 5 '16 at 18:02
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One thought I had, although I have no idea how it would lead to the solution, is that:

All three large circles could actually be the same circle, which is concealed by a rotating disc with three holes. So it would actually be like a clock face, with the numbers 9 2 6 _ 10 1 7 _ ? 3 6 _ appearing in clockwise order, starting from the top.

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  • $\begingroup$ I’m leaning towards that direction as well. It also makes me think we should work in Z / 12 Z, as on a clock. The musician in my ear also cry “serialism”, but I think that my be cultural bias. Still, though, in Z / 12 Z, if you take n(i) for i from 0 to 11 s.t. n(p) ≠ n(q) when p ≠ q and n(p) - n(p-1) ≠ n(q) - n(q-1) when 0 ≠ p ≠ q ≠ 0, then n(12) - n(0) = 6, which would explain the two 6s on the wheel. $\endgroup$ – Édouard May 6 '16 at 10:07
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Another vote for

13

I don't think we have enough numbers/circles to establish a satisfactory pattern, but this is what I went for.

Look at the top left 3 numbers. It's like an arrow with the 3 pointing west. For the circle to its right (clockwise) it's like that arrow has rotated clockwise juuuust a little bit. Then the 3 is replaced by 6, the 2 by the other 6 and 1 by the 7. For the bottom circle you rotate that arrow a little bit again and you replace one 6 with a 9 and the other with 10. Therefore, the patterns are:

3 -> 6 -> 9 (+3)
2 -> 6 -> 10 (+4)
1 -> 7 -> ? (+6)

After posting I realised that

my answer is effectively the same as Gordon's, because you increase the sum of each circle by 13 (3 + 4 + 6). So, we can't pool our answers to say 13 is more likely than other guesses.

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  • $\begingroup$ This is the solution I came to, prior to reading it. $\endgroup$ – Raystafarian May 5 '16 at 18:39
  • $\begingroup$ While I like the idea of the three circles rotating, but I think it lacks the “meta” aspect of the three “large” circles. $\endgroup$ – Édouard May 5 '16 at 21:57
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    $\begingroup$ @Édouard I don't understand what meta aspect you're referring to. Did I miss some context or comment? $\endgroup$ – Reti43 May 5 '16 at 22:21
  • $\begingroup$ I think you should look into a similar relationship between the three “large” circles as well. $\endgroup$ – Édouard May 6 '16 at 9:58
  • $\begingroup$ @Édouard I still don't follow. Can you maybe give an example? With 3 circles, there can be at most 3 relationships, i.e., A to B, B to C and A to C, two of which involve the missing element. I'd argue we don't have enough data to find only a single specific pattern that fits the solution, as demonstrated by various answers here. $\endgroup$ – Reti43 May 6 '16 at 10:02
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One plausible solution is:

13

Because:

The sum of the first circle is 6, the sum of the second is 19, and with 13, the sum of the third is 32. In this case all three circles are in clockwise increasing order with an difference of 13
6 + 13 -> 19 + 13 -> 32

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    $\begingroup$ Well that's two decent answers now which undermines the quality of the puzzle. I think the perfect square answer is too "deep" to be tested. Usually the solution is quite simple. This could be it $\endgroup$ – user1849962 May 5 '16 at 18:10
  • $\begingroup$ @user1849962 I saw mensa and decided to make it complicated xD $\endgroup$ – ChronoD May 5 '16 at 18:12
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    $\begingroup$ @ChronoD yeah when I saw mensa, it made me think my answer was too easy haha $\endgroup$ – Gordon Allocman May 5 '16 at 18:13
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May be it is

13

Reason

There are two sort of z shapes. One reversed, facing each other. The sum of each would be equal if ? is 13

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