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High School
By
Shiva Kintali
on Aug. 28, 2013 | Updated Jan. 4, 2018
7 points inside a hexagon
Consider a hexagon \(H\) with side length 1. Given any 7 points inside \(H\), show that at least two points are separated by a distance of at most 1.
Puzzles
Puzzles
geometry puzzle
pigeonhole principle
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
2
High School
By
Shiva Kintali
on June 24, 2012 | Updated Dec. 6, 2017
Toggling 100 doors
There are 100 doors numbered 1 to 100 in a row. There are 100 people. The first person opens all the doors. The second person closes all the even-numbered doors. The third person changes the state of…
Puzzles
Puzzles
interview question
math puzzle
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
2
Undergraduate
By
JeffE
on June 6, 2012 | Updated Dec. 6, 2017
Longest increasing digital subsequence
Let \(S[1..n]\) be a sequence of integers between \(0\) and \(9\). A digital subsequence of \(S\) is a sequence \(D[1..k]\) of integers such that each integer \(D[i]\) is the numerical value of a sub…
Computer Science
Algorithms
dynamic programming
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
neeldhara
on Aug. 1, 2012 | Updated Dec. 6, 2017
Determining a polynomial
Let \(p\) be a polnyomial with natural coefficients. An oracle can evaluate \(p\) at any value you like. Can you determine all the coefficients by making two queries to the oracle? Note: You are free…
Puzzles
Puzzles
polynomials
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
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