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**miansons****Member**- Registered: 2012-11-25
- Posts: 1

What is the answer to below puzzle? I am unable to solve this.

"A high school has a strange principal. On the first day, he has his students perform an odd opening day ceremony:

There are one thousand lockers and one thousand students in the school. The principal asks the first student to go to every locker and open it. Then he has the second student go to every second locker and close it. The third goes to every third locker and, if it is closed, he opens it, and if it is open, he closes it. The fourth student does this to every fourth locker, and so on. After the process is completed with the thousandth student, how many lockers are open?"

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,705

Hi miansons;

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,394

hi bobbym,

How are you today?

This seems to be a general rule for any number of lockers. But why? hhhmmmm

Bob

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

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,394

Arrh! I've just worked out why.

Bob

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,705

Hi Bob;

I am still chugging along.

But why?

Seek and ye shall find.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,394

I have.

Sorry I double posted.

Bob

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,705

Hi;

The bulb is lit! Very good!

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,525

Hi guys

The reason is that only lockers whose numbers have and odd number of divisors will become open. Showing that only square numbers satisfy this condition is a piece of pie chart.

Hi Bob

Is this what you meant?

*Last edited by anonimnystefy (2012-11-26 01:11:25)*

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

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,848

Hi miansons,

*Last edited by phrontister (2012-11-26 10:04:08)*

"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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,705

Showing that only square numbers satisfy this condition is a piece of pie chart.

Piece of pie chart? That does not sound delicious at all.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,525

Who said it was?

I have to ask you something in the random chatter thread later...

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

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,394

Easy as pie chart!

Look at the time between post 3 and post 4.

Impressive speed huh?

Bob

If only the OP was as quick to respond, sob, sob.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,525

Impressive, indeed. But, why haven't you posted your idea?

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

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,394

Thank you. It is a new policy of mine. If the OP remains silent then I keep my answer to myself.

I've been sitting on the 45 degree plane answer for 24 hours.

http://www.mathisfunforum.com/viewtopic.php?id=18465

Bob

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,525

I can see why you would do that... But, do you really think that there will be an improvement in the response of OPs?

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,705

I have to ask you something in the random chatter thread later...

It better not be my age.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,394

Stefy wrote:

But, do you really think that there will be an improvement in the response of OPs?

No it probably won't. But it will help to stop me getting annoyed when I've spent time on a problem and typing it up and then [blank]

bobbym wrote:

It better not be my age.

But we know you'll never tell that. btw. I'm still working on Phrontister's puzzle.

Bob

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,705

Phrontister is brilliant but standing upside for his entire 28 years has affected his judgement. He believes that he saw me in 1904 at the fair.

His puzzle is going to place me at about 350 years old.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,394

Have you solved his puzzle then ?

I kinow from what I have done so far, that it will not make you more than 100 .

So he couldn't have seen you in 1904.

1913 I could believe.

Bob

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,705

Hi;

No, I have never solved that problem.

1913 is not correct. Phrontister is a good friend and a cousin but he is unable to see the contradiction between my age and my appearance at the fair.

Of course that result can be rigorously obtained, but who cares?

Combinatorics is Algebra and Algebra is Combinatorics.

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,848

bobbym wrote:

He believes that he saw me in 1904 at the fair.

No! No! No! Closure is closure!!

phrontister wrote:

I think that's it, Bobby!

I was probably so swept along with the whole "I've gotta know how old Bobby is and what he looks like" thing here on MIF that my imagination took hold. No other explanation makes sense...so, closure at last!

bobbym wrote:I believe you are probably imagining the whole thing. I mean some people want to believe so bad that they have seen me that they just think they did.

Btw, I improved my C1 formula in my post #9 by removing a duplication, making it more succinct. I'm glad I spotted this now before the OP did.

Hi, Bob. So someone is actually working on my puzzle! When you've solved it, I'd be very interested to see how you went about it.

"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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**mathaholic****Member**- From: Juliania
- Registered: 2012-11-29
- Posts: 2,845
- Website

"Double the fun, double the thrill, double the coolness" - Julianthewiki

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