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**mathenjoyer****Novice**- Registered: 2024-10-08
- Posts: 4

Have this sequence puzzle on a test, can anyone help guess the next number?

4, 6, 2, 8, 3, 9, ?

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**mathenjoyer****Novice**- Registered: 2024-10-08
- Posts: 4

Never mind, I got the answer, it's 1.5

Was a tricky one because I thought it would be an integer solution but it's not!

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**Bob****Administrator**- Registered: 2010-06-20
- Posts: 10,610

hi mathenjoyer

Welcome to the forum!

Well I'm glad you found an answer. I cannot! So how about helping me out here. Where did 1.5 come from?

Bob

Children are not defined by school ...........The Fonz

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

Sometimes I deliberately make mistakes, just to test you! …………….Bob

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**mathenjoyer****Novice**- Registered: 2024-10-08
- Posts: 4

9 / 6 = 1.5!!

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**mathenjoyer****Novice**- Registered: 2024-10-08
- Posts: 4

Thanks for the warm welcome

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,868

mathenjoyer wrote:

9 / 6 = 1.5!!

I think that 9 / 6 follows the correct strategy, but is incorrect because of a small error.

...unless *I'm* wrong!

*Last edited by phrontister (2024-10-09 21:44:28)*

"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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**Bob****Administrator**- Registered: 2010-06-20
- Posts: 10,610

mathenjoyer wrote:

9 / 6 = 1.5!!

Assume I'm really stupid. Please explain what the term to term rule is that generates this sequence. Thanks.

Bob

Children are not defined by school ...........The Fonz

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

Sometimes I deliberately make mistakes, just to test you! …………….Bob

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,868

Hi Bob;

Here's my method...but with a different result from mathenjoyer's:

# Term

The bold numbers are a sequence of 6 numbers from **2** to **7**, and the operators used are the repeating sequence + ÷ × – .

I say 'repeating sequence', as the 5th term repeats the '+' used in the 1st term....from which it follows that the 6th term would use the '÷' from the 2nd term.

*Last edited by phrontister (2024-10-10 22:36:38)*

"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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**Bob****Administrator**- Registered: 2010-06-20
- Posts: 10,610

(1,4) (2,6) (3,2) (4,8) (5,3) (6,9)

bobbym once pointed out that you can always fit a function to any set of six points.

To be a 'solution' there has to be sufficient evidence from the given numbers to find a unique rule that will allow you to determine the next number(s).

I'm impressed with your answer phro. I'd never have got that. But what is the rule that generates 1.5 as the next. I still cannot see it.

Bob

Children are not defined by school ...........The Fonz

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

Sometimes I deliberately make mistakes, just to test you! …………….Bob

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 4,868

Hi Bob;

To be a 'solution' there has to be sufficient evidence from the given numbers to find a unique rule that will allow you to determine the next number(s).

Expressing my method isn't as easy as I'd hoped, but here goes (and I'm sorry, I don't know how to do non-LaTeX subscripts here on MIF):

Rule: Term 1 (t1) = 4, and subsequent terms (t2, t3, etc) follow the [+1] incrementing form { t2 = t1 + t2's term position }, with arithmetic operators for the respective terms being assigned from the repeating sequence { + / * – } (starting with '+' for t2).

Here's my demonstration worksheet for the first 9 terms (note that t6's operator begins the first repeat of the operator sequence):

As you can see from the formulas in column H, calculations for terms after t1 are done entirely in column G. The other columns explain the calculations.

I'd never have got that.

I thought the same about my initial efforts, but then started again with an Excel spreadsheet to help organise & lay out my thoughts.

Light dawned while working out relationships between the adjacent given terms in column G and the various possible ways in which to arrive at each next term. That led to discovering the use of the 4 arithmetic operators, followed by recognising that the group of 4 operators was a repeating sequence.

mathenjoyer wrote:

9 / 6 = 1.5!!

mathenjoyer wrote:Never mind, I got the answer, it's 1.5

I'd really like to know the rule to get that answer!

*Last edited by phrontister (2024-11-07 02:35:40)*

"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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