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**cooljackiec****Member**- Registered: 2012-12-13
- Posts: 185

anonimnystefy wrote:

Hi cooljackiec

I found that these numbers satisfy Q2.

I sort of see what you are doing here, but then again, I don't quite understand. We try to make sure that no numbers in our set are the arithemtic mean of two others. I've been suggested to use base 3, but I don't know how that would work.

EDIT: Turn our set into base 3 integers. Selecting those expressed with only 0 and 1 (base 3) gives us 2^k integers. I think this works, but I have to prove that this satisfies the condition of one number not being the AM of 2 others.

*Last edited by cooljackiec (2014-06-16 17:03:59)*

I see you have graph paper.

You must be plotting something

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,015

That is correct.

Now, think about what a sum of two such number looks like and what twice a such number looks like.

Also, did you see post #25?

*Last edited by anonimnystefy (2014-06-16 22:07:21)*

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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**cooljackiec****Member**- Registered: 2012-12-13
- Posts: 185

The sum of two numbers (in base 3) will have a 2 digit?? Is that what you're saying?

also, 32 is not correct

I see you have graph paper.

You must be plotting something

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,015

It is correct that it will have the digit 2, but what's more imortant is that it will **always** have a 1. Compare that to a double of a number from the sequence.

Hm, you have the correct answer for Q1?

*Last edited by anonimnystefy (2014-06-17 04:42:52)*

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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**cooljackiec****Member**- Registered: 2012-12-13
- Posts: 185

yea, i got the 2nd question, but not the 1st.

I see you have graph paper.

You must be plotting something

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,015

Do you know what the answer is to Q1?

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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**cooljackiec****Member**- Registered: 2012-12-13
- Posts: 185

nope

I see you have graph paper.

You must be plotting something

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,015

Then, how do you know it's not 32?

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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**cooljackiec****Member**- Registered: 2012-12-13
- Posts: 185

The decimal representation of m/n, where m and n are relatively prime positive integers and m<n, contains the digits 2, 5, and 1 consecutively, and in that order. Find the smallest value of n for which this is possible.

I see you have graph paper.

You must be plotting something

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,291

Hi;

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.** **A number by itself is useful, but it is far more useful to know how accurate or certain that number is.**

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,015

Hi bobbym

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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**cooljackiec****Member**- Registered: 2012-12-13
- Posts: 185

I thought that 999 was the answer at first. 800 yields 0.25125. Maybe there's something else in the problem I didn't comprehend. I'm going to get some clarification

I see you have graph paper.

You must be plotting something

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,015

What happened for the first question?

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,291

Hi;

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.** **A number by itself is useful, but it is far more useful to know how accurate or certain that number is.**

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**cooljackiec****Member**- Registered: 2012-12-13
- Posts: 185

so apparently, we can have 2513 and stuff. So like we just need 251 in order and then can have extra digits. 251 /999 is interesting, because 251 is close to 250, a divisor of 1000, which is cllose to 999.

Anyways, idk about the 1st quesiton

EDIT: we don't need to have a repeated decimal

*Last edited by cooljackiec (2014-06-20 08:35:21)*

I see you have graph paper.

You must be plotting something

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,291

so apparently, we can have 2513 and stuff

In that case we can get

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.** **A number by itself is useful, but it is far more useful to know how accurate or certain that number is.**

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,015

Hi bobbym

That seems the smallest so far.

Hi cooljackiec

Well, I asked you multiple times how you know the answer is not 32, without a respense.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,291

Hi anonimnystefy;

The older I get the more I demand rigor. Not in the answer like math types do, but in the question itself!

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,015

Yes, I have noticed.

Do you think there is a smaller answer?

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,291

M does not think so. The last time I disagreed with M and I was right was in July 2001...

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,015

Hm, how did M get that answer?

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,291

It just found a smaller one with an improvement in the logic.

and another one

and another

No mas?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,015

How did you get those?

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,291

Did you see the last one?

```
FindInstance[{m > 0, n > 0, Floor[1000 m/n] == 251, n < 127,
m != n}, {m, n}, Integers]
```

Got to go eat!

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,015

Bon appétit!

That code seems to be slightly incomplete, but fortunately, it does not change the answer.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

The knowledge of some things as a function of age is a delta function.

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