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#26 2014-06-16 15:26:06

cooljackiec
Member
Registered: 2012-12-13
Posts: 178

Re: bases

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
lol

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#27 2014-06-16 22:02:16

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 15,937

Re: bases

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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#28 2014-06-17 04:03:48

cooljackiec
Member
Registered: 2012-12-13
Posts: 178

Re: bases

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
lol

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#29 2014-06-17 04:25:05

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 15,937

Re: bases

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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#30 2014-06-17 14:12:44

cooljackiec
Member
Registered: 2012-12-13
Posts: 178

Re: bases

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


I see you have graph paper.
You must be plotting something
lol

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#31 2014-06-17 14:16:46

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 15,937

Re: bases

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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#32 2014-06-17 15:36:46

cooljackiec
Member
Registered: 2012-12-13
Posts: 178

Re: bases

nope


I see you have graph paper.
You must be plotting something
lol

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#33 2014-06-17 23:23:43

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 15,937

Re: bases

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


“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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#34 2014-06-19 15:43:07

cooljackiec
Member
Registered: 2012-12-13
Posts: 178

Re: bases

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
lol

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#35 2014-06-19 18:52:17

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 96,613

Re: bases

Hi;


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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#36 2014-06-19 22:56:51

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 15,937

Re: bases

Hi bobbym


“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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#37 2014-06-20 03:27:04

cooljackiec
Member
Registered: 2012-12-13
Posts: 178

Re: bases

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
lol

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#38 2014-06-20 03:51:05

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 15,937

Re: bases

What happened for the first question?


“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.

Offline

#39 2014-06-20 04:41:12

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 96,613

Re: bases

Hi;


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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#40 2014-06-20 08:28:46

cooljackiec
Member
Registered: 2012-12-13
Posts: 178

Re: bases

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
lol

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#41 2014-06-20 08:59:21

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 96,613

Re: bases

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.

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#42 2014-06-20 10:29:34

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 15,937

Re: bases

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.


“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.

Offline

#43 2014-06-20 13:18:02

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 96,613

Re: bases

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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#44 2014-06-20 13:26:18

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 15,937

Re: bases

Yes, I have noticed.

Do you think there is a smaller answer?


“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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#45 2014-06-20 14:02:44

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 96,613

Re: bases

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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#46 2014-06-20 14:21:04

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 15,937

Re: bases

Hm, how did M get that answer?


“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.

Offline

#47 2014-06-20 14:33:47

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 96,613

Re: bases

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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#48 2014-06-20 14:39:14

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 15,937

Re: bases

How did you get those?


“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.

Offline

#49 2014-06-20 14:42:16

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 96,613

Re: bases

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.

Offline

#50 2014-06-20 15:05:53

anonimnystefy
Real Member
From: Harlan's World
Registered: 2011-05-23
Posts: 15,937

Re: bases

Bon appétit!

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


“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.

Offline

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