Unsolved Problems
Showing 1-13 of 13 problems
Category
Problem Set
Status
The Hadwiger-Nelson Problem
What is the minimum number of colors needed to color the points of the plane such that no two points at distance 1 have the same color?...
Ramsey Number R(5,5)
What is the exact value of $R(5,5)$, the smallest number $n$ such that any 2-coloring of the edges of $K_n$ contains a monochromatic $K_5$?...
The Lonely Runner Conjecture
For any $n$ runners on a circular track with distinct constant speeds, each runner is "lonely" (distance at least $1/n$ from all others) at some time....
Frankl's Union-Closed Sets Conjecture
For every finite union-closed family of sets (other than the empty family), there exists an element that belongs to at least half of the sets....
Singmaster's Conjecture
Does there exist a finite upper bound on how many times a number (other than 1) can appear in Pascal's triangle?...
No-Three-in-Line Problem
What is the maximum number of points in an $n \times n$ grid with no three collinear?...
Tic-Tac-Toe Winning Dimension
Given the width of a tic-tac-toe board, what is the smallest dimension guaranteeing X has a winning strategy?...
Perfect Chess
What is the outcome of a perfectly played game of chess?...
Perfect Komi in Go
What is the perfect value of komi (compensation points) in Go?...
Octal Games Periodicity
Are the nim-sequences of all finite octal games eventually periodic?...
Grundy's Game Periodicity
Is the nim-sequence of Grundy's game eventually periodic?...
Rendezvous Problem
What is the optimal strategy for two agents to meet on a network without communication?...
1/3-2/3 Conjecture
Does every non-total finite poset have two elements x,y with P(x before y in random linear extension) ∈ [1/3, 2/3]?...