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High School
By
TrueShelf Inc.
on May 27, 2014 | Updated Dec. 6, 2017
JEE-Main 2013 Mathematics 31
The circle passing through \((1, −2)\) and touching the axis of \(x\) at \((3, 0)\) also passes through the point
Mathematics
Geometry
circle
jee
jee main
2
High School
By
TrueShelf Inc.
on Nov. 14, 2016 | Updated Dec. 6, 2017
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 possi…
Mathematics
Combinatorics
imo
imo 2016
polynomials
0
High School
By
TrueShelf Inc.
on July 1, 2017 | Updated Dec. 6, 2017
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
1
High School
By
TrueShelf Inc.
on July 21, 2016 | Updated Dec. 6, 2017
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
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
High School
By
TrueShelf Inc.
on Oct. 21, 2014 | Updated Dec. 6, 2017
Farmers and Chickens
Three farmers were selling chickens at the local market. One farmer had 10 chickens to sell, another had 16 chickens to sell, and the last had 26 chickens to sell. In order not to compete with each …
Mathematics
linear equations
0
Undergraduate
By
TrueShelf Inc.
on May 21, 2014 | Updated Dec. 6, 2017
99 fair coins
Person \(A\) flips 99 fair coins and obtains \(a\) heads. Person \(B\) flips 100 fair coins and obtains \(b\) heads. What is the probability that \(a < b\) ?
Mathematics
Probability
conditional probability
interview question
0
High School
By
TrueShelf Inc.
on June 6, 2014 | Updated Dec. 6, 2017
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
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
0
High School
By
TrueShelf Inc.
on May 29, 2014 | Updated Dec. 6, 2017
JEE-Advanced 2013 Mathematics 55
A rectangular sheet of fixed perimeter with sides having their lengths in the ratio 8 : 15 is converted into an open rectangular box by folding after removing squares of equal area from all four corne…
Mathematics
Geometry
volume
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