- #1

- 365

- 1

## Main Question or Discussion Point

1

2

1 2

4

1 1 3

6

1 2 4

???

What comes next?

2

1 2

4

1 1 3

6

1 2 4

???

What comes next?

- Thread starter Moo Of Doom
- Start date

- #1

- 365

- 1

1

2

1 2

4

1 1 3

6

1 2 4

???

What comes next?

2

1 2

4

1 1 3

6

1 2 4

???

What comes next?

- #2

- 854

- 16

Answer (in white):Moo Of Doom said:1

2

1 2

4

1 1 3

6

1 2 4

???

What comes next?

8 (a partition of 8, but the even numbers are partitioned into a single partition). I haven't figured out how the odd numbers are partitioned, but it seems that the entry for 2^n - 1 is 1 2 4 ... 2^(n-1)

- #3

- 365

- 1

- #4

- 239

- 0

- #5

- 5

- 0

[Answer in white]

Answer: 16

It increases the first number by one then multiply it with the rest.

ie:

1 2 4

(1+1) * 2 * 4 = 16

- #6

- 116

- 0

The answer is 16. Or so I think, if my way is allowed.

1

2

1 2

4

1 1 3

6

1 2 4

???

seperate the lines into groups just to understand it better:

1

2

--------

1 2

4

--------

1 1 3

6

------

1 2 4

???

Multiply the top lines digits by themselves and then by two:

(a*b)*2

so the first line:

(1)*2=2

and the second & third:

(1*2)*2=4

(1*1*3)*2=6

So for the bottom line you get:

(1*2*4)*2=16

Is that a logical answer?

- #7

- 239

- 0

so you are saying that the top line in each group generated by random ?

- #8

- 365

- 1

Maybe there isn't quite enough information.

Here's the pattern a bit longer:

1

2

1 2

4

1 1 3

6

1 2 4

2 6

1 3 5

10

???

What comes next?

- #9

- 854

- 16

Moo, how about more clues, or an answer?

- #10

- 365

- 1

1

2

1 2

4

1 1 3

6

1 2 4

2 6

1 3 5

10

1 1 1 2 6

12

1 5 7

???

Still want a clue? Partitions are correct. But think of the sequence as starting from 2 rather than 1...

- #11

- 12

- 0

a 16 year olds guess....lol

4 10

1 2 4 8

16

??

4 10

1 2 4 8

16

??

Last edited:

- #12

- 365

- 1

Close. The second two are correct, but 4 10 is not. Care to explain your answer?

- #13

- 12

- 0

ok its sumthin like 4 10...but the numbers add up to 14? i spent about 20 mins workin it out lol ill get it when i get time

- #14

- 365

- 1

Yeah, the numbers add up to 14 but they're not 4 10.

- #15

- 12

- 0

is it 2 12?

- #16

- 12

- 0

and *this is gna seem really stupid* but whats partition?

- #17

- 854

- 16

A partition is simply a representation of a positive integer as a sum of other positive integers. For instance 12 = 2 + 10 or 12 = 4 + 8, or 12 = 1 + 2 + 9 or in the degenerate case, 12 = 12. The sequence that Moo has presented us with can be viewed as a sequence of partitions. Here is a list of all the possible partitions of 5:0m3ga said:and *this is gna seem really stupid* but whats partition?

5 = 1 + 1 + 1 + 1 + 1

5 = 1 + 1 + 1 + 2

5 = 1 + 1 + 3

5 = 1 + 4

5 = 1 + 2 + 2

5 = 2 + 3

I hope I didn't miss any. By the way, I didn't know what a partition was until I was about 21, so now you are 5 years ahead of me.

- #18

- 365

- 1

Nope. First number is 2, though.0m3ga said:is it 2 12?

- #19

- 12

- 0

the only reasonable guess i can think off is 2 6 6

- #20

- 365

- 1

Now you're just firing blindly :P

Nope, not 2 6 6.

Nope, not 2 6 6.

- #21

- 12

- 0

i see the whole pattern the only bit i didnt get was the bit where it went 2 6 lol and im guessin thats linked to the line i cant get

- #22

- 68

- 0

I can see that each number that is followed by a prime number is left intact

I think it is based on some method of decomposing the fractions

1/2, 2/3, 3/4, 4/5 etc

I notice that 2/3 can't be broken down

but 3/4 = 1/2 + 1/4

7/8 and 15/16 seem to match your breakdown

when I do 8/9=2/3+2/9 it seems to confirm your partition pattern

BUT

9/10=1/2 +4/10 DOESN'T match up

So I'm missing some other criterion that is not apparent

- #23

NateTG

Science Advisor

Homework Helper

- 2,448

- 5

Let's see here:

2 3 10

1 2 4 8

16

1 1 3 3 9

18

2 3 10

1 2 4 8

16

1 1 3 3 9

18

- #24

- 365

- 1

- #25

- 12

- 0

2 2 10?....

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