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#1 2013-03-22 12:55:27

eagerlearner
Member
Registered: 2013-03-22
Posts: 3

Counting problems, please help...

Bob built a Web site and gave the URL only to his n friends, which he numbered from 1 to n. He
told friend number i that he/she can visit the Web site at most i times. Now Bob has a counter, C,
keeping track of the total number of visits to the site (but not the identities of who visits). What is
the minimum value for C such that Bob should know that one of his friends has visited his/her
maximum allowed number of times?

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#2 2013-03-22 13:01:43

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,562

Re: Counting problems, please help...

Hi eagerlearner;

I am not following you. The first friend ( i = 1 ) can visit at most 1 time. So wouldn't the minimum value of C be 1? That could mean friend #1 has been here the maximum.


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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#3 2013-03-22 13:24:11

eagerlearner
Member
Registered: 2013-03-22
Posts: 3

Re: Counting problems, please help...

and what if "the maximum value of C" is required instead of mimum?

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#4 2013-03-22 14:02:24

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 90,562

Re: Counting problems, please help...

You reason about it like this:

Supposing he had 2 friends.

The bottom row shows the maximum amount they can use the site without exceeding their limit. 0 + 1 = 1. If C is 1 or less than no one has come in to many times.

How about 3 friends:

The maximum amout is 0 + 1 + 2 = 3


For 4 friends:

The maximum number without anyone exceeding his limit is 0 + 1 + 2 + 3 = 6

For 5 friends:

0 + 1 + 2 + 3 + 4  = 10

if their is one more than this number than someone has reached his limit.

Can you finish now?

Last edited by bobbym (2013-03-22 19:21:13)


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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