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**Siva882****Member**- Registered: 2018-05-17
- Posts: 5

1296, 216, 72, 36, 24, ?

'?' Is not 12 or 18. Please help

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**Alg Num Theory****Member**- Registered: 2017-11-24
- Posts: 330
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**Siva882****Member**- Registered: 2018-05-17
- Posts: 5

Nope, they said answer was 20, but our group of 25 members tried to solve it we either got 12 or 18 which is multiple of 6.

Given options are

A. 12 B. 20 c. 6 D. 15 E. 9

*Last edited by Siva882 (2018-05-25 00:22:44)*

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,600

Hi;

I got 18, like so:

Btw, that method gives the next number below 18 as being 16, which seems to be the lowest integer solution and is not a multiple of 6.

I haven't been able to find a method that would get the answer 20.

FWIW, to find the next number above 1296, I used a similar strategy to the one I used above and got 23328, like so:

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,600

Ah, yes...I finally got 20!

Without spoiling all the fun and giving the game away entirely, I'll just say (for now at least) that I saw a hidden pattern of a sequence of fractions, in which:

- the denominator is 1 greater than the numerator; and

- the denominator and numerator are positive integers that are either both 1 greater than, or both 1 less than, the respective elements of adjacent fractions.

*Last edited by phrontister (2018-05-29 21:59:08)*

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,600

Here's my spreadsheet solution. I started writing it all out longhand but got rather tongue-tied, and decided to just go with the simpler presentation.

You'll see that I had to dig down pretty deep to get the answer.

The solution relies on the hidden pattern of fractions mentioned in my previous post:

"... a sequence of fractions, in which:

- the denominator is 1 greater than the numerator; and

- the denominator and numerator are positive integers that are either both 1 greater than, or both 1 less than, the respective elements of adjacent fractions."

No doubt there's a solution much closer to the surface that is simply staring me in the face, but which I'm blind to!

*Last edited by phrontister (2018-05-29 22:00:24)*

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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**Alg Num Theory****Member**- Registered: 2017-11-24
- Posts: 330
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phrontister wrote:

No doubt there's a solution much closer to the surface that is simply staring me in the face, but which I'm blind to!

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,600

Hi Alg Num Theory;

Well, that solution certainly wasn't staring me in the face!

I haven't got the first clue as to what it is or does or how it works, though, as it seems to be way beyond my low maths level (unless I've forgotten it from school).

I'll have to take your word for it that it's a solution.

*EDIT: I entered it into W|A, which gave results (including this puzzle's solution) for the first 15 integer values of n. *

*Last edited by phrontister (2018-05-29 01:00:43)*

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**Alg Num Theory****Member**- Registered: 2017-11-24
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I actually used Wolfram to simplify the following expression (which I had to do in two stages as it was too long for the software to process in one go):

*Last edited by Alg Num Theory (2018-05-30 04:24:34)*

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,600

Sorry, but I don't understand that expression...too advanced for me.

What does your method suggest is the pattern for this sequence?

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**Alg Num Theory****Member**- Registered: 2017-11-24
- Posts: 330
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Sorry, I made some typos in my formula. I’ve edited my post and fixed it now.

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