Impartial Avoidance Games on Convex Geomet
School Name
Hammond School
Grade Level
10th Grade
Presentation Topic
Mathematics
Presentation Type
Mentored
Abstract
We analyze a two-player game in which players take turns avoiding the selection of certain points within a convex geometry. The objective is to prevent the convex closure of all chosen points from encompassing a predefined set. The first player forced into a move that results in the inclusion of this set loses the game. We redevelop a theoretical framework for these avoidance games and determine their nim numbers, including cases involving vertex geometries of trees, edge geometries of trees, and scenarios where the predefined set consists of extreme points.
Recommended Citation
Shim, Seomgeun, "Impartial Avoidance Games on Convex Geomet" (2025). South Carolina Junior Academy of Science. 32.
https://scholarexchange.furman.edu/scjas/2025/all/32
Location
PENNY 203
Start Date
4-5-2025 10:45 AM
Presentation Format
Oral and Written
Group Project
No
Impartial Avoidance Games on Convex Geomet
PENNY 203
We analyze a two-player game in which players take turns avoiding the selection of certain points within a convex geometry. The objective is to prevent the convex closure of all chosen points from encompassing a predefined set. The first player forced into a move that results in the inclusion of this set loses the game. We redevelop a theoretical framework for these avoidance games and determine their nim numbers, including cases involving vertex geometries of trees, edge geometries of trees, and scenarios where the predefined set consists of extreme points.
