Exercises
Multiple Choice
Articles
Open Problems
Login
187 exercises
Subject:
Mathematics
Start over
- to expand, or dig in by adding more tags and revising the query.
Sort By:
trending ▼
date
3
High School
By
True IMO
on Nov. 14, 2016 | Updated Jan. 4, 2018
International Mathematical Olympiad 2016 Problem 5
The equation \((x-1)(x-2)(x-3)...(x-2016) = (x-1)(x-2)(x-3)...(x-2016)\) is written on a board, with 2016 linear factors on each side. What is the least possible value of \(k\) for which it is p…
Mathematics
Combinatorics
imo
imo 2016
polynomials
1
High School
By
True IMO
on July 1, 2017 | Updated Jan. 4, 2018
International Mathematical Olympiad 2015 Problem 2
Determine all triples of positive integers such that each of the numbers is a power of 2.
Mathematics
Algebra
imo
imo 2015
0
Undergraduate
By
rizwanhudda
on Aug. 24, 2012 | Updated Dec. 6, 2017
Second Minimum spanning tree
Given an weighted undirected graph \( G = (V, E)\), and \(w : E \mapsto R^+\). Let T be MST i,e minimum spanning tree of graph G. Second MST is a Tree T' different from T, and its weight is less t…
Computer Science
Mathematics
Algorithms
Graph Theory
trees
0
Undergraduate
By
John Doe
on Nov. 3, 2012 | Updated Dec. 6, 2017
Direct reduction from Graph Homomorphism to SAT
The decision problem \(GraphHomo\) is defined as follows: \(GraphHomo = \{\langle G, H\rangle \mid \text{there is a graph homomorphism from G to H}\}\) Give a direct reduction from \(GraphHomo\) to …
Computer Science
Mathematics
Complexity Theory
Graph Theory
Logic
np
reduction
sat
0
Undergraduate
By
Chandra Chekuri
on July 29, 2012 | Updated Dec. 6, 2017
Simple path containing three given nodes
Let \(G=(V,E)\) be an undirected graph. Describe a linear time algorithm that given \(G\) and three distinct nodes \(u,v,w\) decides whether there is a simple path in \(G\) that contains all of them.
Computer Science
Mathematics
Algorithms
Graph Theory
linear time algorithms
2
High School
By
True IMO
on July 21, 2016 | Updated Jan. 4, 2018
International Mathematical Olympiad 2016 Problem 3
Let \(P = A_1, A_2 \dots A_k\) be a convex polygon on the plane. The vertices \(P = A_1, A_2 \dots A_k\) have integral coordinates and lie on a circle. Let \(S\) be the area of \(P\). An odd positive …
Mathematics
Geometry
imo
imo 2016
polygon
0
Undergraduate
By
diego
on June 8, 2012 | Updated Dec. 6, 2017
The cube of a connected graph is hamiltonian
Prove that the vertices of any connected graph \(G\) can be listed in a cyclic order so that the distance in \(G\) of every two consecutive vertices is at most \(3\). Moreover, show that this can be …
Computer Science
Mathematics
Algorithms
Graph Theory
hamiltonian cycle
0
Undergraduate
By
diego
on June 27, 2012 | Updated Dec. 6, 2017
Unmatchable edges of bipartite graphs
Prove that the following algorithm finds the unmatchable edges of a bipartite graph \(G\) (edges that aren't in any perfect matching): find a perfect matching in \(G\), orient the unmatched edges from…
Mathematics
Graph Theory
bipartite graph
matching
0
Undergraduate
By
Chandra Chekuri
on July 29, 2012 | Updated Dec. 6, 2017
Diameter and low-degree vertex
Let \(G = (V,E)\) be an undirected connected graph. Suppose \(G\) has a pair of nodes \(s,t\) that are distance \(d\) apart. Show that there is a vertex \(v\in G\) such that the degree of \(v\) is at…
Computer Science
Mathematics
Algorithms
Graph Theory
counting
0
High School
By
Shiva Kintali
on June 6, 2014 | Updated Jan. 4, 2018
Constructible polygons
A constructible polygon is a regular polygon that can be constructed with compass and straightedge. For example, a regular pentagon is constructible with compass and straightedge while a regular hepta…
Mathematics
Geometry
polygon
1
2
3
...
17
18
19
next page »
icon
Sign In or Sign Up
icon
Invite Friends
Post Something
x
Select What You'd Like To Post
POST AN ARTICLE
POST AN OPEN PROBLEM
POST AN EXERCISE
POST A MULTIPLE-CHOICE QUESTION
Content Types
Articles
Open Problems
Exercises
Multiple-Choice Questions
Levels
High school
Undergraduate
Graduate
Subjects
Mathematics
Computer Science
Puzzles
Optimization
Trending tags
formal languages
trees
dynamic programming
polynomials
infinite series
digraphs
fermats little theorem
asymptotic analysis
differentiation
integration
Topics
Algebra
Algorithms
Approximation Algorithms
Calculus
Combinatorial Optimization
Combinatorics
Complexity Theory
Data Structures
Discrete Mathematics
Game Theory
Geometry
Graph Theory
Linear Algebra
Linear Programming
Logic
Mathematical Analysis
Mathematics
Matrix Theory
Number Theory
Optimization
Probability
Programming
Puzzles
Randomized Algorithms
Real Analysis
Trigonometry
×