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#1 2016-11-17 09:43:46

Mathegocart
Member
Registered: 2012-04-29
Posts: 2,226

Problems in Math Competition:

Today I took a intriguing mathematical quiz(cannot disclose: sorry!)
Anyhow I feel like it devastated me, and I have two questions that were perplexing, namely..
1) Andy and Barry are running around a circular track that is 400 ft. Andy and Barry start at the same place, though Barry pulls up, travelling at 125% the speed of Andy. How many laps of the track has he traversed once Barry surpasses Andy?

2) There are 216 sprinters participating in a race. Unfortunately, the track only holds 6 people at a time. Once a sprinter wins the race, the others are eliminated. This process is reiterated until a final champion wins. How many races are held to find the champion?


The integral of hope is reality.
May bobbym have a wonderful time in the pearly gates of heaven.
He will be sorely missed.

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#2 2016-11-17 12:04:25

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Problems in Math Competition:

Hi;




In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#3 2016-11-17 22:43:00

Mathegocart
Member
Registered: 2012-04-29
Posts: 2,226

Re: Problems in Math Competition:

bobbym wrote:

Hi;



ARGH! I had attained that solution though I doubted myself and picked 44. sad


The integral of hope is reality.
May bobbym have a wonderful time in the pearly gates of heaven.
He will be sorely missed.

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#4 2016-11-17 22:51:36

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Problems in Math Competition:

Overconfidence is a serius weakness but lack of confidence is death.

Never doubt yourself.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#5 2016-11-17 23:16:09

Mathegocart
Member
Registered: 2012-04-29
Posts: 2,226

Re: Problems in Math Competition:

The sad thing was that I spent too much time on the 125% problem)(which was problem 19/25) and I unfortunately didn't have time to finish the rest. sad
Also, I have another problem.
3) There are 3 nickels and 2 pennies in a bag. A man draws coins out of the bag without replacement. He stops when all 3 nickles or 2 pennies are drawn out.  What is the probability that he pulls 3 nickels?
A: Obviously this is quite simplistic: 3/5*2/4*1/3 = 1/10, though the answer choices do not concur(there was no 1/10 as a choice.). Am I simply missing an obvious step? I want some confirmation.

Last edited by Mathegocart (2016-11-17 23:26:59)


The integral of hope is reality.
May bobbym have a wonderful time in the pearly gates of heaven.
He will be sorely missed.

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#6 2016-11-17 23:34:59

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Problems in Math Competition:

Urn, bag, box, bucket... problems are never simplistic.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#7 2016-11-18 02:23:56

Mathegocart
Member
Registered: 2012-04-29
Posts: 2,226

Re: Problems in Math Competition:

bobbym wrote:

Urn, bag, box, bucket... problems are never simplistic.

Could you confirm that?


The integral of hope is reality.
May bobbym have a wonderful time in the pearly gates of heaven.
He will be sorely missed.

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#8 2016-11-18 11:00:15

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Problems in Math Competition:

Hi;


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#9 2016-11-18 21:17:38

thickhead
Member
Registered: 2016-04-16
Posts: 1,086

Re: Problems in Math Competition:


{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

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#10 2016-11-18 21:20:14

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Problems in Math Competition:

Hi;

If you just blurt out the answer like that how is he supposed to learn to think for himself? As a teacher you should know that.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#11 2016-11-18 21:36:24

thickhead
Member
Registered: 2016-04-16
Posts: 1,086

Re: Problems in Math Competition:

I have not given the answer. It was you.That is only one way thinking.One could think in other ways also like a problem of combinations only.


{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

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#12 2016-11-18 23:59:55

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Problems in Math Competition:

I gave that answer because only by showing someone the hard way encourages them to look for something easier. If you would have read my post #8 you would have seen that I wanted him to examine the problem and look for that shortcut on his own.

You gave a detailed solution and the answer over here:
http://www.mathisfunforum.com/viewtopic … 79#p390579

All that person has to do is just copy it and use it on a test or in his homework.

This forum has already been accused of encouraging cheating because full solutions are given and they only need to be able to cut and paste what is posted here. It is of course not your concern how the forum appears to teachers in general, it is mine. For one thing on all other forums that I am a member of they follow this rule for questions: No work, no answer.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#13 2016-11-19 01:21:40

Mathegocart
Member
Registered: 2012-04-29
Posts: 2,226

Re: Problems in Math Competition:

bobbym wrote:

Hi;

Hmmm, I will try to find a more intuitive way.. I felt like it was so simplistic I dismissed it as trivial..


The integral of hope is reality.
May bobbym have a wonderful time in the pearly gates of heaven.
He will be sorely missed.

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#14 2016-11-19 01:24:06

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Problems in Math Competition:

Think about it for a bit. I expect that you can get it on your own.

If you get stuck take a look at all the possibilities that can happen.

{5, 5, 5, 1, 1}
{5, 5, 1, 5, 1}
{5, 5, 1, 1, 5}
{5, 1, 5, 5, 1}
{5, 1, 5, 1, 5}
{5, 1, 1, 5, 5}
{1, 5, 5, 5, 1}
{1, 5, 5, 1,  5}
{1, 5, 1, 5, 5}
{1, 1, 5, 5, 5}

What do you notice when the 3 fives run out first?


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#15 2016-11-19 01:45:56

Mathegocart
Member
Registered: 2012-04-29
Posts: 2,226

Re: Problems in Math Competition:

bobbym wrote:

Think about it for a bit. I expect that you can get it on your own.

If you get stuck take a look at all the possibilities that can happen.

{5, 5, 5, 1, 1}
{5, 5, 1, 5, 1}
{5, 5, 1, 1, 5}
{5, 1, 5, 5, 1}
{5, 1, 5, 1, 5}
{5, 1, 1, 5, 5}
{1, 5, 5, 5, 1}
{1, 5, 5, 1,  5}
{1, 5, 1, 5, 5}
{1, 1, 5, 5, 5}

What do you notice when the 3 fives run out first?

Then there are solely pennies left.


The integral of hope is reality.
May bobbym have a wonderful time in the pearly gates of heaven.
He will be sorely missed.

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#16 2016-11-19 08:23:28

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Problems in Math Competition:

That is correct. So what is the chance that the last one is a penny?


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Offline

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