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Problem 4 Suppose we have a 3x9 grid of 27 squares, where each square is either orange or black. That is, the grid has 9 columns, each with 3 rows. For example, it's possible that all 27 squares are orange, that all 27 square are black, or any combination of orange or black. Use the Pigeonhole Principle to prove that there are two columns that have the same colour pattern (e.g. if one is orange, orange, black, then the other is also orange, orange, black, in the same order.)

Problem 4 Suppose we have a 3x9 grid of 27 squares, where each square is either orange or black. That is, the grid has 9 columns, each with 3 rows. For example, it's possible that all 27 squares are orange, that all 27 square are black, or any combination of orange or black. Use the Pigeonhole Principle to prove that there are two columns that have the same colour pattern (e.g. if one is orange, orange, black, then the other is also orange, orange, black, in the same order.)

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.2: Direct Methods For Solving Linear Systems
Problem 3CEXP
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Problem 4 Suppose we have a 3x9 grid of 27 squares, where each square is either orange or black. That is, the grid has 9 columns, each with 3 rows. For example, it's possible that all 27 squares are orange, that all 27 square are black, or any combination of orange or black. Use the Pigeonhole Principle to prove that there are two columns that have the same colour pattern (e.g. if one is orange, orange, black, then the other is also orange, orange, black, in the same order.)
Transcribed Image Text:Problem 4 Suppose we have a 3x9 grid of 27 squares, where each square is either orange or black. That is, the grid has 9 columns, each with 3 rows. For example, it's possible that all 27 squares are orange, that all 27 square are black, or any combination of orange or black. Use the Pigeonhole Principle to prove that there are two columns that have the same colour pattern (e.g. if one is orange, orange, black, then the other is also orange, orange, black, in the same order.)
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