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#26 2009-12-23 14:19:20

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,594

Re: What do you think?

Do you see the pattern that all the solutions have?


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#27 2009-12-23 15:35:20

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 3,853

Re: What do you think?

I think so.

Let's say that:
y = the smallest answer x, and
z = 434782608695652173913


For any of the answers x, the next-highest answer is:

(x * 10^(the number of digits in (y * z))) + (y * z)

I don't think that wording's too clever - but I hope you know what I mean. I'll try to tidy it up with an edit if you don't beat me to it. Maybe using a subscript 'n' for x would do it, but I haven't worked out how to display that yet - or if that's the way to do it.

Last edited by phrontister (2009-12-23 16:27:44)


"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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#28 2009-12-23 16:26:09

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,594

Re: What do you think?

Hi phrontister;


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#29 2009-12-23 16:38:02

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 3,853

Re: What do you think?

Nice! That works perfectly.

It's the senior version of the junior version I used to find my first answer

Last edited by phrontister (2009-12-23 16:43:22)


"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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#30 2009-12-23 18:55:43

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 88,594

Re: What do you think?

Hi phrontister;

Thats very clever, someone on another forum did exactly that.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#31 2009-12-23 21:33:04

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 3,853

Re: What do you think?

Hi Bobby,

...someone on another forum did exactly that.

Must be my twin brother - we think alikn (sic). wink I hadn't seen that site before - some interesting characters there!

Good question by the OP, too, asking for the problem to be solved without using a calculator!

No - I came up with my wonderful solution all on my own (must have been holding my calculator downside-up just at the right moment of inspiration to think of the inversion).


"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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#32 2009-12-23 23:50:35

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,594

Re: What do you think?

Hi phrontister;

I hadn't seen that site before - some interesting characters there!

No one interesting over there.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#33 2009-12-24 12:25:31

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 3,853

Re: What do you think?

Hi Bobby,

No one interesting over there.

Yes...I'm losing interest. There seems to be only one genuine bogus imposter there - not very exciting.


"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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#34 2009-12-27 05:18:50

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,594

Re: What do you think?

Hi;

Problem #8:

How high can you go? If you don't know the rules then go here:

http://nrich.maths.org/786

I've given you a starter puzzle, it sums to 66. You should be able to beat that,

View Image: Untitled.gif

In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#35 2010-01-01 01:20:35

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,594

Re: What do you think?

Hi;

Problem #9:

Try this one on for size, it is quite easy. Which is larger and why?


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#36 2010-01-01 13:16:03

JaneFairfax
Member
Registered: 2007-02-23
Posts: 6,868

Re: What do you think?

bobbym wrote:

Hi;

Try this one on for size, it is quite easy. Which is larger and why?

Last edited by JaneFairfax (2010-01-01 13:16:23)


Q: Who wrote the novels Mrs Dalloway and To the Lighthouse?

A: Click here for answer.

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#37 2010-01-04 01:31:44

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,594

Re: What do you think?

Hi Jane;

Yes, you are right. Well done!


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#38 2010-01-04 03:48:57

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 3,853

Re: What do you think?

Hi Bobby,

76.

This one's just a variation of my pattern for the 6-number daisy that scored 46 in the Number Daisy and Proof? thread. I haven't tried any other options yet.

View Image: Daisy-7.png

Last edited by phrontister (2010-01-04 19:48:22)


"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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#39 2010-01-05 15:23:19

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,594

Re: What do you think?

Hi phrontister;

Good work! It is what I have.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#40 2010-01-05 15:45:45

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 3,853

Re: What do you think?

Hi Bobby,

I thought that basing the answer to this 7-number puzzle on the (currently) highest-scoring 6-number one would be a good place to start...but I have no way of proving maximums for either form.

I've tried several other options since, including a central 2, 3 and 4, but got nowhere.

Last edited by phrontister (2010-01-05 15:54:42)


"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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#41 2010-01-05 19:25:23

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,594

Re: What do you think?

Hi phrontister;

but I have no way of proving maximums for either form.

I am in the same spot.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#42 2010-01-06 21:17:06

gibbo
Member
Registered: 2010-01-06
Posts: 1

Re: What do you think?

Hi Bobby
to yield nines (problem 17?). Use multiples of 23. The clue is that the number is 21 digits long. It would have been more obvious if it had been 22 digits long. eg 1304347826086956521739

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#43 2010-01-07 00:01:25

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,594

Re: What do you think?

Hi gibbo;

Welcome to the forum!

gibbo wrote:

to yield nines (problem 17?). Use multiples of 23.

Not all multiples of 23 will yield  all nines.

The next number that yields all nines after 23 is:

23 000 000 000 000 000 000 00 23

Here is another problem:

This one is so, so.

An urn contains 15 balls. There are only 2 different colors the balls can have, red and orange. There are at least 3 of each color in the urn. Picking 3 balls without replacement. the probability that all of the picked ones are red is the same as the probability that exactly one of them is orange. How many of the 15 balls are red?


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#44 2010-01-11 11:12:36

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,594

Re: What do you think?

Problem #10:

Two people pick six numbers from the set {1,2,3,4,5,...44} with replacement. What is the probability that they have the same six numbers?

Person A says the probability that they have the same six numbers is:

Person B says the probability that they have the same six numbers is:

The textbook says .0000102

Who is right?


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#45 2010-01-13 21:44:58

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,594

Re: What do you think?

Problem #11:

In Clare's math class there are 2 times as many 11 th-grade students as there are 9 th and 10th grade students combined. Then there are 2 times as many 12th grade students as 9th grade students. The number of 11th grade students is 10 times the number of 12th grade students. Altogether there are 32 students in Clare's math class, How many are there of each?


Problem #12:

An urn contains 15 balls. There are only 2 different colors the balls can have, red and orange. There are at least 3 of each color in the urn. Picking 3 balls without replacement. the probability that all of the picked ones are red is the same as the probability that exactly one of them is orange. How many of the 15 balls are red?


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

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#46 2010-01-14 01:04:12

phrontister
Real Member
From: The Land of Tomorrow
Registered: 2009-07-12
Posts: 3,853

Re: What do you think?

Hi Bobby,

Clare's maths class

Last edited by phrontister (2010-01-14 03:32:56)


"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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#47 2010-01-14 04:36:51

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,594

Re: What do you think?

Very good, that is correct.


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#48 2010-01-15 02:44:07

JaneFairfax
Member
Registered: 2007-02-23
Posts: 6,868

Re: What do you think?

bobbym wrote:

An urn contains 15 balls. There are only 2 different colors the balls can have, red and orange. There are at least 3 of each color in the urn. Picking 3 balls without replacement. the probability that all of the picked ones are red is the same as the probability that exactly one of them is orange. How many of the 15 balls are red?

Suppose there are n red balls (
). The probability of picking 3 red balls is
. The probability of picking exactly one orange ball is
. Hence, if they are equal, we have
.


Q: Who wrote the novels Mrs Dalloway and To the Lighthouse?

A: Click here for answer.

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#49 2010-01-15 03:44:57

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,594

Re: What do you think?

Hi Jane;

So good to see you. Yes! There is no solution, n must be an integer.

This is a variant of a problem posed on another forum that was too easy. So I adjusted the numbers hoping to make it somewhat confusing. I can't point to the link because that page is not coming in right now. Anyway, because his problem was so easy it succumbed to a brute force attack. I believe the first one I tried was the answer. I don't like problems that the poser never even considers a simplistic method of solution. I posed mine to force the solver to do something other than trying one example.

Well done!


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

#50 2010-01-15 04:20:10

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,594

Re: What do you think?

Hi Jane;

Here is the link:

http://www.artofproblemsolving.com/Foru … p?t=323599

Too easy!!!

Since we are discussing pieces of the balls in the urn , you did make a slight arithmetic error. Do you see it?


In mathematics, you don't understand things. You just get used to them.

I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.

Offline

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