Problems with a Point

The following sections are included:

• Preface
• Acknowledgments
• Contents

The following sections are included:

• Point
• n + 1
• Quantum
• Prisoner’s Dilemma
• Turing Test
• Venn Diagram
• Zeno’s Paradox
• Have Any of These Phrases Entered the Mainstream?
• References

The following sections are included:

• Point
• Baseball Violates the Pythagorean Theorem: Home Plate
• Baseball Violates The Laws of Statistics: Batting Averages
• Target: 3000 Hits in a Career
• Target: 300 Wins in a Career
• The (Il)logic of Fandom

The following sections are included:

• Point
• A Set of Logicians
• Some Comments on Section 3.2
• References

The following sections are included:

• The Question
• The Answer and the Point
• Comments on Section 4.2
• A Nonpattern: Regions in a Circle
• More Nonpatterns: Borwein Integrals
• References

The following sections are included:

• Point
• Name the Theorem After the Person Who Proved it
• Name the Mathematical Object After Euler or Gauss
• Hope Someone Names Your Theorem After You
• Math Objects Named Descriptively
• Math Objects Named For a Funny Reason
• Names Change: Conjecture to Theorem
• Names Change: Historical Accuracy
• References

The following sections are included:

• Point
• The First Batch of Talks from G4G12
• Some More On Gathering for Gardner
• I Was Inspired
• References

The following sections are included:

• Point
• Every Planar Graph is 4.5-Colorable — A Personal History
• The Definition of Fractional Coloring
• References

The following sections are included:

• Point
• Introduction
• Pre-Christian History of England
• Ramsey Theory
• Kneading’s Book
• Simplification Due to Ramsey’s Theorem
• Open Problems
• Acknowledgements
• References

The following sections are included:

• Story and Point
• Later Renditions
• References

The following sections are included:

• Rant
• Hey Wait a Minute!
• A Barrier Identified and Overcome: The Erdős Distinct Distance Problem
• Comments From The Readers
• References

The following sections are included:

• Point
• The University of Maryland High School Mathematics Competition
• Cans of Paint
• Points in the Plane
• The Real Answers
• References

The following sections are included:

• The Point
• The Problems
• The c = 2 Case
• The c = 3 Case
• Exact Bounds for the c = 3 Case
• The c = 4 Case
• The c = 4 Case
• Formal Statement of the Polynomial van Der Warden Theorem
• References

The following sections are included:

• The Point
• Notation and Helpful Lemma
• Four Correct Solutions and An Interesting Incorrect Solution
• SOLUTION ONE-1 and SOLUTION ONE-2
• For all a, SOLUTION ONE-a
• Improving the Base Case
• Another Infinite Set of Proofs
• For 1 ≤ a ≤ 149 What is the Smallest n₀?
• Article vs. Blog
• The Students Answers to Part (a)

The following sections are included:

• The Point
• Solution by William Gasarch
• Solution by Sam Zbarsky
• Solution by David Eppstein
• More Bounds on cool(n)
• Recap
• Open Questions
• References

The following sections are included:

• Point
• The Two-Digit Lemma
• The Main Theorem
• For the Reader

The following sections are included:

• The Point
• The Problems
• My Solution and Interest Level
• The Riddler Said … Was it Interesting?
• What Makes a Good Puzzle
• Research Questions Inspired by the Puzzle
• References

A Hat Problem: Assume n people are standing in a line, each facing the person in front of him. Each person is wearing either a RED hat or a BLUE hat. We will call the person who sees everyone in front of him the first person. He sees all of the hats except his own. The next person, who sees all but two hats, we call the second person, etc. The last person cannot see any hats…

The following sections are included:

• Point
• The Questions
• Answers
• References

The following sections are included:

• Points
• A FUN Problem in Multiparty Communication
• A FUN Solution
• A Sequel You Can Ask a Civilian
• Is the Problem Fun? An Experiment
• Multiparty Communication Complexity: A Serious Approach
• Open Problems
• The Original Worksheet
• References

The following sections are included:

• Point
• Notation
• Proof by Algebra and Induction That $\left(\begin{array}{c}2n\\ n\end{array}\right)$ is an Integer
• Proof by Number Theory That $\left(\begin{array}{c}2n\\ n\end{array}\right)$ is an Integer
• Combinatorial Proof That C_n, the nth Catalan Number, is an Integer
• Proof by Number Theory That C_n is an Integer
• Open Problem

The following sections are included:

• Point
• The Problem
• Needed Theorems
• The Main Theorem
• Is the Theorem Interesting?

The following sections are included:

• Point
• Is COL₄ ≤ COL₃?
• The Reduction Made Some Students Sad :-(
• Yes There is a Sane Reduction
• References

The following sections are included:

• Point
• Motivation
• Our Main Tool to Show Grids are Not c-Colorable
• Our Main Tool to Show Grids are c-Colorable
• Which Grids are 2-Colorable?
• Which Grids Can be 3-Colored?
• Which Grids Can be 4-Colored?
• It’s a Floor Wax! It’s a Dessert Topping! It’s Both!
• Open Questions
• References

The following sections are included:

• Point
• How to Measure Randomness Intuitively
• A Short Introduction to Computability Theory
• Intermediary Sets
• How to Measure Randomness Formally
• Is the Kolmogorov Function Intermediary?
• The Point Reiterated
• References

The following section is included:

• Index