Number series puzzle

[Lehmund]

When I first gave 3 Small Eberron Dragonshards to the collector in Market named Peta (somethingorother), in exchange for an Eladrin shrine token, she game me a number series puzzle. Being a math teacher, I thought to myself "heck, cool, maybe I get a bonus."

Turns out its not an easy one. Or at least the solution I came up with (after it expired as I got a call while figuring out and Peta told me it took me too much time... grrr), seems a bit too complex for a game. here goes, you guys can give me feedback, or if someone did solve this one before, you could confirm the solution:

Series:
18, 9, 6

My solution is 5.

Reasoning:
18 - 3^2= 9
9 - 3^1= 6
6 - 3^0= 5

The reason I think it seems too complex, and why I think there may be another solution I don't see, is that the concept of a "0" exponent = 1 is not exactly mainstream, even though it IS high school level (at least up here in Ontario, Canada).

Is 5 the solution? Is there a simpler one my math brain just can't see?

Cheers!

[caius15]

i would try 4.5

f(x)=18x^(-1)

but then again as it doesn't mean anything. There is as many solution that match those 3 points that people on this forum...

[Loraf]

I would say 3

18/3 = 6
9/3 = 3

18 9 6 3

[Kreaper]

I say 42.

[ThrasherGT]

I say 42.

"Don't Panic!"

"Earth: Mostly Harmless."

[Cedwin]

Series:
18, 9, 6

My solution is 5.

Reasoning:
18 - 3^2= 9
9 - 3^1= 6
6 - 3^0= 5

I'd say 4.5

18/1 = 18
18/2 = 9
18/3 = 6
18/4 = 4.5

[Tumarek]

3 numbers are really not enough to give a qualified answer imho.

could be pretty much anything:

18 / 2 = 9
9 / 1.5 = 6
6 / 1 = 6

and so on....

[paul1devries]

i would say 3 as well:

18 9 6

1. 9 is half of 18
2. 6 is 18/3

if you put in 3 next then
1. 3 is half of 6
2. 3 is 9/3

[Gornin]

3 is my answer too.

[Ozmoth]

Being a math teacher, I thought to myself "heck, cool, maybe I get a bonus."

seems a bit too complex for a game. here goes, you guys can give me feedback, or if someone did solve this one before, you could confirm the solution:

I Applaud your efforts sir but, I am gonna say KISS. I do believe you overthought that one just a touch. It happens. 3 for the win.

[Cedwin]

i would say 3 as well:

18 9 6

1. 9 is half of 18
2. 6 is 18/3

if you put in 3 next then
1. 3 is half of 6
2. 3 is 9/3

The answer has to follow a pattern, I don't see a pattern according to your math for the answer 3.

18/2 = 9
18/3 = 6
9/3 = 3
6/2 = 3

[rimble]

The answer has to follow a pattern, I don't see a pattern according to your math for the answer 3.

18/2 = 9
18/3 = 6
9/3 = 3
6/2 = 3

Even not nerding out on it and figuring it out, 3 just makes too much sense combined with 6, 9, and 18, regardless of not having the formula worked out. I really can't see how it could be 4 or 5, maybe 2, but the 9 kinda complicates that, and 1 may be the next thing after 3, but not after 6.

Fuzzy math FTW!

[Grond]

18/3=6
9/3=3
6/3=2
3/3=1

6=1+2+3
3=2+1


I would expect the next number up in the series to be 3x(6+3+2+1), or 36.

However, the OP's postulate holds water as well, and may actually be more proper. He's extrapolating down from 18, I reverse engineered from a theoretical start point. I looked at it almost as a bastardized Fibinacci series, where you state the beginning and derive based off that. His manipulated what was already there.

[Grond]

It could even be
(3^2)x2 18
(3^2)x1 9
(3^1)x2 6
(3^1)x1 3

Further extrapolation downward would yield results of 2 and 1 ((3^0)x2, (3^0)x1).

[Cedwin]

It could even be
(3^2)x2 18
(3^2)x1 9
(3^1)x2 6
(3^1)x1 3

Further extrapolation downward would yield results of 2 and 1 ((3^0)x2, (3^0)x1).

Either way, all of the answers listed are mathematically correct, but this one seems to follow the simplest pattern.

18 / 1 = 18
18 / 2 = 9
18 / 3 = 6
18 / 4 = 4.5

or

18 / 2 = 9
9 / 1.5 = 6
6 / 1 = 6

or

3 * (1) = 3
3 * (1+1) = 6
3 * (1+(1+1)) = 9
3 * (1+(1+1)+(1+(1+1))) = 18

[Anderei]

The progression formula is:

x[n+1]=x[n]/3+3

Its divided by 3 plus 3 to get to the next number in the series.

18 / 3 +3 = 9
9 / 3 + 3 = 6
6 / 3 + 3 = 5.

5 is the correct answer.

4.6666 would be the next after that.
45 would come before the 18 if you want to give more numbers.

Altough this formula is simpler, interestingly enough Lehmund system yields the same results 4.6666 and 45 for next and previous number. Its up the reader to determine why both systems are apparently equivalent (because I don't know how to prove it :-)

[paul1devries]

Can somone just go do it and tell us what answer is?

To respond to Cedwins question about no pattern in my answer...

To get to 3 as the answer, I used the three number string to get a pattern as 18-9-6 did not follow a simple progression (single number by single number). I looked at all three numbers to deduce next number so 9 is half of 18 and 6 is 1/3 of 18. Therefore the next number (now using 9-6-answer being solved for) would be 3 as 3 is half of 6 and 1/3 of 9.

A number of other answers could also theoretically be the right answer as well as shown - usually on a test of some sort, you would need enough answers shown to make sure there are not multiple solutions, but here, with the numbers shown , there still are multiple possibilities.

I prefer 3 as being relatively the most simple solution but would love to hear what Turbine decided.

[Anderei]

Can somone just go do it and tell us what answer is?

To respond to Cedwins question about no pattern in my answer...

To get to 3 as the answer, I used the three number string to get a pattern as 18-9-6 did not follow a simple progression (single number by single number). I looked at all three numbers to deduce next number so 9 is half of 18 and 6 is 1/3 of 18. Therefore the next number (now using 9-6-answer being solved for) would be 3 as 3 is half of 6 and 1/3 of 9.

A number of other answers could also theoretically be the right answer as well as shown - usually on a test of some sort, you would need enough answers shown to make sure there are not multiple solutions, but here, with the numbers shown , there still are multiple possibilities.

I prefer 3 as being relatively the most simple solution but would love to hear what Turbine decided.

Not quite if 18 is the base of your first set.

18/2 = 9
18/3 = 6

And you now use 9 as the base of your next set it would be:
9 / 2 = 4.5 (and this is a contradiction, since it must be a 6 to follow 18 9 6 rule)
9 / 3 = 3

Your system is contradicts itself.

To correct it, you could at least use 6 as the base of the next set
6 / 2 = 3
6 / 3 = 2.

Then two for the next set. This would give at least a self-sustaining system, altough IMHO not the simplest one, and making a set as large as the numbers given, gives for every numver series a logical explanation, no art here.

I could as well say, a set is -9 and -12

18 - 9 = 9
18 - 12 = 6

First set, second:
6 - 9 = -3
6 - 12 = -18

and so on.

Or I could say with the same logic (assuming a set is as large as the given numbers) the series is simply:
18 9 6 18 9 6 18 9 6 18 9 6 18 9 6 18 9 6 18 9 6 18 9 6

18/1 = 18
18/2 = 9
18/3 = 6
18/4 = 4.5

This is IMHO the only valid alternative solution to the 5 been posted so far by OP and me
The only thing about this: 4.5 is not a nice natural number and i suppose it was not an answer option, right?

/ 3 + 3, simplest way to go

[Dyesalot]

Sometimes the simplest is not the best and that is all I am saying on that matter.

Still trying but dang those fragments are hard to come by. Tried 2 times and nothing so far. Wont spoil the quest for others so if your looking for the answer keep searching

[ehcsztein]

I would expect the next number up in the series to be 3x(6+3+2+1), or 36.

However, the OP's postulate holds water as well, and may actually be more proper. He's extrapolating down from 18, I reverse engineered from a theoretical start point. I looked at it almost as a bastardized Fibinacci series, where you state the beginning and derive based off that. His manipulated what was already there.

I followed similar logic and came up with the following expanded series...

...144,72,36,18,9,6,3

Which could be generated by...


Taken from
http://www.wolframalpha.com/input/?i...%2C9%2C18%2C36

I have not been able to get other options listed to generate a function yet. Then again my math abilities are weaksauce at best *shrug*