MathDB
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 10\sqrt{10} 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?