Pigeonhole Principle: consider the 3D grid with integer coordinates (That is, a point (x, y, z) lies on the grid if and only if x, y and z are all integral). Prove that if we take nine points on the grid then there exist two of the points whose average is also a point on the grid.
Pigeonhole Principle: consider the 3D grid with integer coordinates (That is, a point (x, y, z) lies on the grid if and only if x, y and z are all integral). Prove that if we take nine points on the grid then there exist two of the points whose average is also a point on the grid.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 74E
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Pigeonhole Principle: consider the 3D grid with integer coordinates (That is, a point (x, y, z) lies on the grid if and only if x, y and z are all
average is also a point on the grid.
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