# 1-8, what's the next number?

$1, 2, 3, 4, 5, 6, 7, 8, X, 9, 10, 11, 12 ?$

What is the number x in the above series?

Hint: It's not 9.

Hint 2:

there is a reason that the series is a series of continuous from 1 to 8.

Hint 3:

there is something with the numbers of digits.

Hint 4:

position index. Here 8th term is 8 but 9th term can not be 9, instead the 10th term is 9.

Hint5:

after "x" the series again continues till it reaches the 99th term and then 999th term and so on..

Final Hint: No more hints after this (it was asked to us when i was in 7th grade)

98th and 99th terms are 97 each. 100th term is 98.

• As show the answers, you should at least point where to think. Because there's indefinite number of approaches... – nicael Jun 10 '16 at 20:52
• "I know, it's 10 because its the next number x for which 840/x is an integer!" – palsch Jun 10 '16 at 20:58
• It's not 9, because 7-ate-9! So the next one must be 10 – Inazuma Jun 11 '16 at 3:21
• number of natural numbers less than n+2 not in ( 10^m for whole m) – Jasen Jun 12 '16 at 2:39
• the 9th term must be 8, 9+2=11, the numbers less than 11 not in 10^m are 2,3,4,5,6,7,8,9 - of which there are 8. – Jasen Jun 13 '16 at 12:43

as this question hase ben taken off hold I'll post my answer

it's

8

because the sequence is

$$s(n) = n-floor(log_{10}(n+1))$$

I think it is

nine, although you say it's not

because

Wolfram|Alpha says this and Wolfram|Alpha never lies. :P

Look:

• Your infallible reference also believes that $\small\sf s,a,n,t,a,c,l,a,u,s \to 1/10 (3a{+}c{+}l{+}n{+}2s{+}t{+}u) = 1/6 (e{+}i{+}2s{+}t{+}x) \to e,x,i,s,t,s,...$ – humn Jun 10 '16 at 22:34
• @humn Of course. W|A is always right, so he exists. Didn't you know? – palsch Jun 11 '16 at 11:28
• @humn Santa Claus may exist! wolframalpha.com/input/?i=Does+Santa+Claus+exist%3F – palsch Jun 11 '16 at 14:20

If it's not nine, than it's

ten, the numbers could be just the 9-base ;P

• I was just thinking this and then your answer popped up. :) +1 – palsch Jun 10 '16 at 20:38
• @nicael there is a sequence which matches all and the next number.. can u justify this with 10? – Wasiq Shahrukh Jun 10 '16 at 20:41
• What could else it be if you're just counting and there's no 9 in 9-base? – nicael Jun 10 '16 at 20:42
• @nicael lateral thinking man – Wasiq Shahrukh Jun 10 '16 at 20:45
• It's ten in base nine, what's wrong... – nicael Jun 10 '16 at 21:07

nothing ?

because

This are numbers of planets in the solar system, Mercury=1, Venus=2, Earth=3, ...

and

so

It's not nine (anymore).

Maybe it is

$0$? And the sequence are numbers modulo $9$.