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**master****Member**- Registered: 2005-08-04
- Posts: 23

I got this problem with no answers.

somebody please help me. it goes like this:

What is the next number in this sequence: 1, 2, 5, 12, 1, 13, 30, 49, 1127, 1156, 1125?

help

thanx

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**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

The graphing function in Excel says that the sequence doesn't have a pattern in a polynomial of an order less than 7, and it's not a linear, power or exponential function. It is possible to create a pattern to fit the sequence, but it will probably involve x^10 and be very horrible in general. The next number in the sequence would probably be a fraction as well. I can't see any obvious pattern, so I think it's probably got some obscure non-mathematical reasoning behind it. If you tell us where you got the puzzle from, we might be able to help more.

Why did the vector cross the road?

It wanted to be normal.

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**master****Member**- Registered: 2005-08-04
- Posts: 23

it's from a contest online. what i posted previously was all that was to the question. the sequence looks kind of odd, so i reckon there is a "semi-mathematical" sequence behind it. do you have any suggestions what the next number can be, just any random suggestion?

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**kylekatarn****Member**- Registered: 2005-07-24
- Posts: 445

depends on the type of approch you make to that data...

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**master****Member**- Registered: 2005-08-04
- Posts: 23

i see what you mean. still having some ideas are better then nothing right?

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,626

Another thought (not follwed up):

1, 2, 5, 12,

1, 13, 30, 49,

1127, 1156, 1125, ????

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

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**master****Member**- Registered: 2005-08-04
- Posts: 23

i kind of thought about that, but the first two lists they just increase all the way, and the last one decrease to 1125 from 1156. another mystery.

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**wcy****Member**- Registered: 2005-08-04
- Posts: 117

the fifth term is really weird (1) and last term

cos other than the fifth and last term, the sequence is generally increasing

there are also a few perfect squares hidden in the sequence, eg

1, 25, 121, 49, 1156

*Last edited by wcy (2005-08-04 23:43:38)*

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**Robin****Guest**

hi,

New to the forum and thought I'd add my 1pence worth.

I have been unable to find the most likely number that is required, but with sequences, there generally isnt only a single no. that is correct. Any number can be written as the next and even proof provided for it being there.

A good way of identifying sequences is to use finite differences. I at first tried this method and it failed to provide a concrete algo, *but* it did show me a pattern.

I haven't had my daily intake of coffee, so forgive any errors (Like spotting the obvious)

Finite differences work on apply subsequent differences between no.s .. Im only interested in the first interation for my example.

1, 2, 5, 12, 1, 13, 30, 49, 1127, 1156, 1125 (Original)

1 3 7 -11 12 17 19 1078 29 -31 (Difference)

Ok notice that the difference gives the answer to the next no.

Starting difference 1+2=3 +2=5+7=12+-11 = 1 etc

Now I havent looked properly, there may be a hidden pattern in the difference which points to the desired next difference (Need Coffee) but the answer can be any no.

Lets say the next sequence is 1094. This would make the difference -31.

so 1125 + -31 = 1094

Anyway, thats my thoughts, good luck and pls take a look at my post I need your help.

Robin

**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 21,484

Good post, and Welcome, Robin!

Subsequent differences, yes, sometimes they do help in find the next number in sequences.

But, what you have pointed out is, I feel, not acceptable.

You have found the difference, and then added that to the previous term.

In mathematical terms, you have found the difference between 2 terms, a and b, then added the difference to a, which would have to be b!

It is no good to try to stop knowledge from going forward. Ignorance is never better than knowledge - Enrico Fermi.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**wcy****Member**- Registered: 2005-08-04
- Posts: 117

1, 2, 5, 12, 1, 13, 30, 49, 1127, 1156, 1125?

i found this pattern:

split the numbers into groups of 3, and multiply their digits together

1

2

5 (1+2²=5)

1x2=2

1

1x3=3 (2+1²=3)

3*0=0

4x9=36, 3x6=18, 1x8=8

1*1*2*7=14, 1*4=4 (0+8²=64=4(take last digit))

1*1*5*6=30, 3*0=0

1*1*2*5=10, 1*0=0

0+0²=0

hence the answer can be any 4 digit number whose digits multiply to 0 eg. 1110.

that is the only pattern i managed to find..

but i suspect that it is significant for 1156 to be a perfect square

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**master****Member**- Registered: 2005-08-04
- Posts: 23

hmm... nice wcy. i m pretty sure that the pattern you found is no coincidence. im now looking deeper through the hints you gave me. there must be more factors to determine the next number....

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**kylekatarn****Member**- Registered: 2005-07-24
- Posts: 445

where did you get this sequence?

I would like to visit the website you took this from

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**master****Member**- Registered: 2005-08-04
- Posts: 23

www.mathwizz.com

but you need a user id and pass word you can use mine

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**kylekatarn****Member**- Registered: 2005-07-24
- Posts: 445

You didn't have to post you login info. The signup is free so I created an account for myself.

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**master****Member**- Registered: 2005-08-04
- Posts: 23

oh ok

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**kylekatarn****Member**- Registered: 2005-07-24
- Posts: 445

the website is very cool it has a lot of math contests!

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**master****Member**- Registered: 2005-08-04
- Posts: 23

i'm not sure if its a coincidence, but look what i just found:

the last 2 numbers of sequence is "1156, 1125" add their first 2 values, or ones, gives us 256 and 225, which turns out to be both perfect square, and in order: they are 14,15 (14^2, 15^2)

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**master****Member**- Registered: 2005-08-04
- Posts: 23

I Mean 16,15 Sorry

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**kylekatarn****Member**- Registered: 2005-07-24
- Posts: 445

how do you apply that rule involving the other numbers?

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**master****Member**- Registered: 2005-08-04
- Posts: 23

i dont know it was just for fun sortof

i was looking at the numbers and was adding stuff and found it. i didnt expect it to work

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**kylekatarn****Member**- Registered: 2005-07-24
- Posts: 445

Could it be this?

We have the following data,where Z is the unknown term

1;2;5;12;1;13;30;49;1127;1156;1125;Z

Lets create groups of 4

```
1 1 1127
2 13 1156
5 30 1125
12 49 Z
```

Let's perform a subtraction

12-5-2-1=4

49-30-13-1=5

If this is the pattern the we can write

Z-1125-1156-1127=6

Z=3414

Althought 3414 doesn't look like 1127, 1156 and 1125, but does that matters? The numbers in the group {1,2,5,12} are also different.

The last term doesn't have to start with 11(...)

I think it's a simple but logic answer.

*Last edited by kylekatarn (2005-08-05 14:01:09)*

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**master****Member**- Registered: 2005-08-04
- Posts: 23

very reasonable if you ask me but apparently not

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**kylekatarn****Member**- Registered: 2005-07-24
- Posts: 445

I'm really stuck on this...

The site's problems are more *'math-based'* or *'logic-based'*?

(This one seems more logic-based.)

*Last edited by kylekatarn (2005-08-06 01:19:56)*

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**master****Member**- Registered: 2005-08-04
- Posts: 23

yeah thats waht i think

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