Continue this series

Reboot It · 2003-06-30, 16:38

You are welcome to puzzle over this series. Despite the short excerpt shown, it is possible to work out the basis of the series from just these four numbers.

2
4
6
30

What comes next? How is the series constructed? Be warned - it may not be quite what you think!

If you know straightaway, please do not spoil it for others: just post the fact in the thread and either withhold the answer for a couple of days or send me a private message with your answer.

If there are no responses I may add some further numbers later. Enjoy!

Jwb52z · 2003-06-30, 19:02

I think the next number should be 210.

eepiccolo · 2003-06-30, 19:07

How about 98?

cheesehead · 2003-06-30, 19:53

Quote:

If there are no responses I may add some further numbers later.

Not too soon!

Xyzzy · 2003-06-30, 20:19

I think I got the answer, but I cheated and looked it up so now I feel all guilty...

xilman · 2003-07-01, 11:54

As the answer to the ultimate question to life, the universe and everything is 42, your series must be the quartic (6 + 70x - 110x^2 + 53x^3 - 7x^4)/3 evaluated at 0, 1, 2, 3, ...

Paul

(The above answer indicates why I loathe questions like this appearing in IQ tests.)

koal · 2003-07-01, 12:04

I agree with eepiccolo: the next number is 98, followed by 232, 454, 786, ...

The Cubic

y = (11x^3 -66x^2 +127x -66) / 3

does this for x = 1, 2, 3, 4, ...

;) 2*7^2

Reboot It · 2003-07-01, 13:41

Well I'm sorry to disappoint you all, but nobody has yet posted the correct answer in this thread. I have received a number of private messages, but I shan't disclose them here (yet).

I'll leave it another day or so before posting on how the series continues. (Oh I love keeping all these brilliant minds in suspense!

)

koal · 2003-07-01, 15:22

Next try: :idea:

The first two elements are 2 and 4. Every element with an index > 2 is created by adding the element i-1 and the factorial of i-2, which gives the sequence:
1) => 2
2) => 4
3) => 6=4+2!
4) => 30=6+4!
5) => 750=30+6!
6) => 265252859812191058636308480000750=750+30!

...

Okkie? 8)

hyh1048576 · 2003-07-01, 15:32

What about 2,4,6,30,180,1470,14850,......?

Reboot It · 2003-07-02, 13:49

Well, I'm quite pleased that this little teaser has generated a little flurry of interest here. I think it is time to tell you a little bit more.

I'm sorry that nobody has yet posted in this thread how the sequence continues, and all of the numbers put forward as putative subsequent members of the series do not actually appear anywhere in the series, with the exception of 42, although it is not the next number in the series but appears later.

Some clues: The solution does not involve a polynomial at all. The series cannot be proved, or even formulated, inductively. Knowing what is not involved should help all you puzzlers still out there.

I will leave it to public demand to see whether you want some further numbers in the series...

2003-06-30, 16:38	#1
Reboot It Aug 2002 London, UK 7×13 Posts	Continue this series You are welcome to puzzle over this series. Despite the short excerpt shown, it is possible to work out the basis of the series from just these four numbers. 2 4 6 30 What comes next? How is the series constructed? Be warned - it may not be quite what you think! If you know straightaway, please do not spoil it for others: just post the fact in the thread and either withhold the answer for a couple of days or send me a private message with your answer. If there are no responses I may add some further numbers later. Enjoy!

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2003-06-30, 19:02	#2
Jwb52z Sep 2002 798₁₀ Posts	I think the next number should be 210.

2003-06-30, 19:07	#3
eepiccolo Dec 2002 Frederick County, MD 2×5×37 Posts	How about 98?

2003-06-30, 20:19	#5
Xyzzy "Mike" Aug 2002 8224₁₀ Posts	I think I got the answer, but I cheated and looked it up so now I feel all guilty...

2003-07-01, 11:54	#6
xilman Bamboozled! "𒉺𒌌𒇷𒆷𒀭" May 2003 Down not across 2A01₁₆ Posts	As the answer to the ultimate question to life, the universe and everything is 42, your series must be the quartic (6 + 70x - 110x^2 + 53x^3 - 7x^4)/3 evaluated at 0, 1, 2, 3, ... Paul (The above answer indicates why I loathe questions like this appearing in IQ tests.)

2003-07-01, 12:04	#7
koal Nov 2002 Vienna, Austria 41 Posts	I agree with eepiccolo: the next number is 98, followed by 232, 454, 786, ... The Cubic y = (11x^3 -66x^2 +127x -66) / 3 does this for x = 1, 2, 3, 4, ... ;) 2*7^2

2003-07-01, 13:41	#8
Reboot It Aug 2002 London, UK 7×13 Posts	Well I'm sorry to disappoint you all, but nobody has yet posted the correct answer in this thread. I have received a number of private messages, but I shan't disclose them here (yet). I'll leave it another day or so before posting on how the series continues. (Oh I love keeping all these brilliant minds in suspense! )

2003-07-01, 15:22	#9
koal Nov 2002 Vienna, Austria 41 Posts	Next try: :idea: The first two elements are 2 and 4. Every element with an index > 2 is created by adding the element i-1 and the factorial of i-2, which gives the sequence: 1) => 2 2) => 4 3) => 6=4+2! 4) => 30=6+4! 5) => 750=30+6! 6) => 265252859812191058636308480000750=750+30! ... Okkie? 8)

2003-07-01, 15:32	#10
hyh1048576 Jun 2003 2⁶ Posts	What about 2,4,6,30,180,1470,14850,......?

2003-07-02, 13:49	#11
Reboot It Aug 2002 London, UK 7×13 Posts	Well, I'm quite pleased that this little teaser has generated a little flurry of interest here. I think it is time to tell you a little bit more. I'm sorry that nobody has yet posted in this thread how the sequence continues, and all of the numbers put forward as putative subsequent members of the series do not actually appear anywhere in the series, with the exception of 42, although it is not the next number in the series but appears later. Some clues: The solution does not involve a polynomial at all. The series cannot be proved, or even formulated, inductively. Knowing what is not involved should help all you puzzlers still out there. I will leave it to public demand to see whether you want some further numbers in the series...