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

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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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,362

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.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 85,362

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.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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