Sequence puzzle (quite hard)

Brendan O'Mahony

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Mar 21, 2004, 10:44:06 PM3/21/04

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Whats the next number in this sequence? (with a reason)
8,5,1,10,4,7,6,2,3,11,?

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r.e.s.

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Mar 22, 2004, 2:36:05 PM3/22/04

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"Arthur J. O'Dwyer" <a...@nospam.andrew.cmu.edu> wrote ...

>
> On Sun, 21 Mar 2004, Brendan O'Mahony wrote:
> >
> > Whats the next number in this sequence? (with a reason)
> > 8,5,1,10,4,7,6,2,3,11,?
>

> 9, because, well, duh? Or were you looking for a more obscure
> answer?

Yup, 9 is what I get too ;o)
Here's a formula for this sequence:

x[n] =
+8*C(n,0)
-3*C(n,1)
-1*C(n,2)
+14*C(n,3)
-42*C(n,4)
+94*C(n,5)
-183*C(n,6)
+323*C(n,7)
-521*C(n,8)
+771*C(n,9)
-1067*C(n,10)

where C(n,k) = n!/(k!(n-k)!), n = 0, 1, 2, 3, ...

This is from a simple html page with javascript that I wrote
for fun some time ago. (Of course it will give an interpolating
polynomial for whatever terms we want to follow the 11.) For
anyone who wants it, I've put the html page at
http://r.s.home.mindspring.com/Interpolate/interpolate.htm

--r.e.s.

Gary Shannon

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Mar 22, 2004, 4:40:56 PM3/22/04

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omah...@hotmail.com (Brendan O'Mahony) wrote in message news:<2723d40c.04032...@posting.google.com>...

> Whats the next number in this sequence? (with a reason)
> 8,5,1,10,4,7,6,2,3,11,?

Using a finite differences triangle to derive a 9th degree equation in
n, the next n yeilds f(n)=1076, so that must be the answer! ;-)

Here are the finite differences with the number series f(n) down the
leftmost column.. Each number is the sum of the number above and the
number diagonally above and right:

8 -3 -1 14 -42 94 -183 323 -521 771
5 -4 13 -28 52 -89 140 -198 250 771
1 9 -15 24 -37 51 -58 52 1021
10 -6 9 -13 14 -7 -6 1073
4 3 -4 1 7 -13 1067
7 -1 -3 8 -6 1054
6 -4 5 2 1048
2 1 7 1050
3 8 1057
11 1065
1076

--gary

r.e.s.

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Mar 22, 2004, 5:35:48 PM3/22/04

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"Gary Shannon" <fiz...@yahoo.com> wrote ...
> omah...@hotmail.com (Brendan O'Mahony) wrote ...

> > Whats the next number in this sequence? (with a reason)
> > 8,5,1,10,4,7,6,2,3,11,?
>
> Using a finite differences triangle to derive a 9th degree equation in
> n, the next n yeilds f(n)=1076, so that must be the answer! ;-)
>
> Here are the finite differences with the number series f(n) down the
> leftmost column.. Each number is the sum of the number above and the
> number diagonally above and right:
>
> 8 -3 -1 14 -42 94 -183 323 -521 771
> 5 -4 13 -28 52 -89 140 -198 250 771
> 1 9 -15 24 -37 51 -58 52 1021
> 10 -6 9 -13 14 -7 -6 1073
> 4 3 -4 1 7 -13 1067
> 7 -1 -3 8 -6 1054
> 6 -4 5 2 1048
> 2 1 7 1050
> 3 8 1057
> 11 1065
> 1076

Yup, 1076 is what I get too ;o)

Here's a formula for this sequence:

x[n] =
+8*C(n,0)
-3*C(n,1)
-1*C(n,2)
+14*C(n,3)
-42*C(n,4)
+94*C(n,5)
-183*C(n,6)
+323*C(n,7)
-521*C(n,8)
+771*C(n,9)

where C(n,k) = n!/(k!(n-k)!), n = 0, 1, 2, 3, ...

Bob Harris

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Mar 22, 2004, 6:52:24 PM3/22/04

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Brendan O'Mahony posted:

> Whats the next number in this sequence? (with a reason)
> 8,5,1,10,4,7,6,2,3,11,?

At least this one's different than the last three you posted.

ObPuzzle: What's the next letter in this sequence?

D O O F U ?

Bob H

Dave Bell

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Mar 22, 2004, 11:40:37 PM3/22/04

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Heh...

'S', of course...

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Brendan O'Mahony

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Mar 25, 2004, 7:11:03 PM3/25/04

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Hard luck lads, the answer is 8.
The sequence is the next months with a Friday the 13th.
So my list starts off with August 2004 and finishes with November
2009, which makes the one after that August 2010 i.e. 8.

Bob Harris

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Mar 27, 2004, 9:59:09 AM3/27/04

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Arthur J. O'Dwyer wrote:

> Sorry, I'm almost positive the answer Bob had in mind was 'V'.
> Better luck next time.

The correct answer is 6.3. Hard luck, lads.

Bob H