Math Prize 2022 Problem 16
Source:
October 12, 2022
Problem Statement
A snail begins a journey starting at the origin of a coordinate plane. The snail moves along line segments of length and in any direction such that the horizontal and vertical displacements are both integers. As the snail moves, it leaves a trail tracing out its entire journey. After a while, this trail can form various polygons. What is the smallest possible area of a polygon that could be created by the snail's trail?