Partial Generalization of ISL '94 C5

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Nirjhor
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Partial Generalization of ISL '94 C5

Unread post by Nirjhor » Tue Jan 20, 2015 1:34 pm

Suppose $2n$ girls are seated around a circle $(n\in\mathbb N).$ One of the girls is given $2n$ coins initially. In a move, each girl with at least $2$ coins passes one coin to each of her two neighbors. The game terminates if, in a move, no girl is able to pass any coins. Prove that the game can't terminate.
Last edited by Nirjhor on Wed Jan 21, 2015 10:42 pm, edited 1 time in total.
- What is the value of the contour integral around Western Europe?

- Zero.

- Why?

- Because all the poles are in Eastern Europe.


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*Mahi*
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Re: Partial Generalization of ISL '94 C5

Unread post by *Mahi* » Wed Jan 21, 2015 2:13 pm

Are you sure about it? ISL 1994 C5 says that the game must terminate with coins $ <2n$ and cannot terminate with exactly $2n$ coins.
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Nirjhor
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Re: Partial Generalization of ISL '94 C5

Unread post by Nirjhor » Wed Jan 21, 2015 3:03 pm

That's why I said *partial*.
- What is the value of the contour integral around Western Europe?

- Zero.

- Why?

- Because all the poles are in Eastern Europe.


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*Mahi*
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Re: Partial Generalization of ISL '94 C5

Unread post by *Mahi* » Wed Jan 21, 2015 6:30 pm

And what I said is that your statement directly contradicts the statement of the ISL problem.
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Nirjhor
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Re: Partial Generalization of ISL '94 C5

Unread post by Nirjhor » Wed Jan 21, 2015 10:42 pm

Sorry, typo, fixed. :|
- What is the value of the contour integral around Western Europe?

- Zero.

- Why?

- Because all the poles are in Eastern Europe.


Revive the IMO marathon.

Nirjhor
Posts:136
Joined:Thu Aug 29, 2013 11:21 pm
Location:Varies.

Re: Partial Generalization of ISL '94 C5

Unread post by Nirjhor » Sat Feb 28, 2015 8:00 pm

Hint
This is a number theory problem. ;)
- What is the value of the contour integral around Western Europe?

- Zero.

- Why?

- Because all the poles are in Eastern Europe.


Revive the IMO marathon.

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