#### Submission Title

#### 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 College 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