# Haters will say 28 June

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.

• How relevant is the title? – Brandon_J Feb 17 '19 at 22:55
• @Brandon_J Very relevant :) – Arvasu Kulkarni Feb 18 '19 at 8:31
• I am thinking that it has linkages to rot13 (Uvccnfhf naq Veengvbany Ahzoref) but I could not decipher the link to the title yet – Kryesec Feb 20 '19 at 2:10
• @Kryesec think of ratios – Arvasu Kulkarni Feb 20 '19 at 3:35
• I wish I saw hints when I posted lmao. – Rigidity Feb 21 '19 at 21:53

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 $$2+7=9$$.

• You got it, well done! 😃 – Arvasu Kulkarni Feb 21 '19 at 1:51

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.

• No, but that’s an interesting coincidence that is really cool once you know the rule. :) – Arvasu Kulkarni Feb 18 '19 at 3:24

Is it:

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

• No, use the subtle hints. :) – Arvasu Kulkarni Feb 18 '19 at 3:23
• @ArvasuKulkarni is 13 the correct answer? – CodeBoyCode Feb 20 '19 at 16:23
• @CodeBoyCode No. – Arvasu Kulkarni Feb 20 '19 at 16:25

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?

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?

• There are 2 numbers? Beware spoilers in my comment 12 and 18 – Yout Ried Feb 20 '19 at 1:11
• What’s the relevance of the title here? – Krad Cigol Feb 20 '19 at 1:43