Submission Title

Competitive Tiling

Location

Jereld R. Nicholson Library

Subject Area

Mathematics

Description

Competitive tiling consists of two players, a tile set, a region, and a non-negative integer d. Alice and Bob, our two players, alternate placing tiles on the untiled squares of the region. They play until no more tiles can be placed. Alice wins if at most d squares are untiled at the end of the game, and Bob wins if more than d squares are untiled. For given regions and tile sets we are interested in the smallest value of d such that Alice has a winning strategy. We call this the game tiling number. In this project, we focus on finding the game tiling number for the game played with dominoes on 2 x n rectangles, modified 2 x n rectangles, and rectangular annular regions.

Comments

Presenter: Levi A. Altringer

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May 16th, 4:30 PM May 16th, 6:00 PM

Competitive Tiling

Jereld R. Nicholson Library

Competitive tiling consists of two players, a tile set, a region, and a non-negative integer d. Alice and Bob, our two players, alternate placing tiles on the untiled squares of the region. They play until no more tiles can be placed. Alice wins if at most d squares are untiled at the end of the game, and Bob wins if more than d squares are untiled. For given regions and tile sets we are interested in the smallest value of d such that Alice has a winning strategy. We call this the game tiling number. In this project, we focus on finding the game tiling number for the game played with dominoes on 2 x n rectangles, modified 2 x n rectangles, and rectangular annular regions.