4
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Find the next number in this sequence:

$4,3,7,5,10,15,?$

Think outside the frustum here.

Hint 1:

This has to do with a ratio that is of a kind that Pythagoras and his followers didn’t like.

Hint 2:

The title is double the key to the puzzle.

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  • 1
    $\begingroup$ How relevant is the title? $\endgroup$ – Brandon_J Feb 17 at 22:55
  • $\begingroup$ @Brandon_J Very relevant :) $\endgroup$ – Arvasu Kulkarni Feb 18 at 8:31
  • $\begingroup$ I am thinking that it has linkages to rot13 (Uvccnfhf naq Veengvbany Ahzoref) but I could not decipher the link to the title yet $\endgroup$ – Kryesec Feb 20 at 2:10
  • $\begingroup$ @Kryesec think of ratios $\endgroup$ – Arvasu Kulkarni Feb 20 at 3:35
  • $\begingroup$ I wish I saw hints when I posted lmao. $\endgroup$ – Rigidity Feb 21 at 21:53
6
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Is the answer:

9? Using Hint 2, the key to the puzzle is $\pi$ since $(\dfrac{1}{2} * 6.28 = 3.14)$. Comparing the differences between the nth digit of the sequence and the nth digit of pi results in the natural numbers $1,2,3,...$. As such, the next digit is the 7th digit of $\pi$ plus 7, which is $2+7=9$.

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  • 1
    $\begingroup$ You got it, well done! 😃 $\endgroup$ – Arvasu Kulkarni Feb 21 at 1:51
4
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This may be too obvious, but a possible answer is:

6

Reasoning:

Given that 4+3=7 and 5+10=15, the sequence can be interpreted in the form of advancing triplets of the form a+b=c. Since a in each triplet goes up by one, that gives 6 as the next value.

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  • $\begingroup$ No, but that’s an interesting coincidence that is really cool once you know the rule. :) $\endgroup$ – Arvasu Kulkarni Feb 18 at 3:24
1
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Is it:

13. 4,x,7,x,10,x,13? Just a thought!

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  • $\begingroup$ No, use the subtle hints. :) $\endgroup$ – Arvasu Kulkarni Feb 18 at 3:23
  • $\begingroup$ @ArvasuKulkarni is 13 the correct answer? $\endgroup$ – CodeBoyCode Feb 20 at 16:23
  • $\begingroup$ @CodeBoyCode No. $\endgroup$ – Arvasu Kulkarni Feb 20 at 16:25
1
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Possible solution. I do not have very much basis to give this answer, but I thought I would throw it out there.

Sorry if this is incorrect.

Given that the series is 4,3,7,5,10,15,?, And 4+3=7, 7+5-2=10, Would the next item be 10+15-4=21?

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1
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I thought this was too obvious but I don't know.

How about 12? Both the addition and subtraction seem to go up. 4-1, 7-2. 3+4, 5+5, 10+5. I was thinking that the amount of addition was going up by one each time. So, as if it was going: Take once, Add once, Take once, Add twice, take once. The next digit would then be 18, if I'm right?

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  • $\begingroup$ There are 2 numbers? Beware spoilers in my comment 12 and 18 $\endgroup$ – Yout Ried Feb 20 at 1:11
  • $\begingroup$ What’s the relevance of the title here? $\endgroup$ – Krad Cigol Feb 20 at 1:43

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