Faculty Sponsor(s)
Michael Hitchman & Chuck Dunn
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.
Recommended Citation
Altringer, Levi A.; Hitchman, Michael P.; Dunn, Charles; Bright, Amanda; Clark, Greg; Evitts, Kyle; Keating, Brian; and Whetter, Brian, "Competitive Tiling" (2014). Linfield University Student Symposium: A Celebration of Scholarship and Creative Achievement. Event. Submission 21.
https://digitalcommons.linfield.edu/symposium/2014/all/21
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.
Comments
Presenter: Levi A. Altringer