Natalia I. Córdova Sánchez
Project Description
My project this summer is based on a two-person game called the Nagger-Mover game. In this game, there are n chairs arranged in a circle which are labeled with the numbers 0, 1, ..., n-1. In the beginning of the game, Nagger is sitting in seat 0 and takes turns sitting in other seats. The Nagger and Mover take turns playing. In each turn, the Nagger says the number of places he wants to move and the Mover tells him in which direction the Nagger should move, either Clockwise or Anti-clockwise. The goal of the Nagger is to maximize the number of chairs he sits on, while the Mover's aim is to minimize it. In this game there are no restrictions of time, in the amount of moves, or in the number of times the Nagger visits a particular seat.
We know that if the number of seats is a prime number, then there is a strategy for the Mover that assures that Nagger will not visit, at least, one of the seats. Also, there is a strategy for the Nagger that assures that he will visit, at least, all but one seats. One of my goals for this summer is to improve the strategy for the Nagger by reducing the number of moves he needs to make in order to sit in n-1 seats.
References
Z. Neved and S. Muthukrishnan. The Nagger-Mover Game. DIMACS Technical Report, 2005-22.
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Natalia I. Córdova
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