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## #1 2013-03-23 11:55:27

eagerlearner
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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?

## #2 2013-03-23 12:01:43

bobbym

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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 have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

## #3 2013-03-23 12:24:11

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

## #4 2013-03-23 13:02:24

bobbym

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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 (2013-03-23 18:21:13)

In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.