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High School
By
TrueShelf Inc.
on Aug. 20, 2013 | Updated Jan. 16, 2017
Bug in a cube
A bug is sitting in one corner of a cube-shaped room. What is the shortest path to go to the extreme opposite corner (i.e., the corner that is farthest) ?
Puzzles
Puzzles
geometry puzzle
interview question
0
Undergraduate
By
Shiva Kintali
on May 19, 2013 | Updated Jan. 16, 2017
Counting intersections of chords
Consider \(n\) chords on a circle, each defined by its endpoints. Describe an \(O(n{\log}n)\)-time algorithm to determine the number of pairs of chords that intersect inside the circle. For example, i…
Computer Science
Algorithms
Data Structures
counting
sorting
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Undergraduate
By
TrueShelf Inc.
on Sept. 30, 2013 | Updated Jan. 16, 2017
Friends and Parties
Show that at a party of \(n\) people, there are two people who have the same number of friends in the party. Assume that friendship is symmetric. There are \(2n\) people at a party. Each person has a…
Mathematics
Discrete Mathematics
counting
pigeonhole principle
0
Graduate
By
Shiva Kintali
on Oct. 12, 2012 | Updated Jan. 16, 2017
Guess the average
Consider the following one-shot game : Each of \(n\) people announces a number in the set \({1,2,\dots,K}\). A prize of \(\\)1{,}000…
Mathematics
Game Theory
nash equilibrium
0
Undergraduate
By
Shiva Kintali
on May 31, 2012 | Updated Jan. 16, 2017
Party Problem
Suppose there are six people at a party. Prove that there are always three of them so that every two know each other (or) no two know each other. In other words, let the edges of the complete graph o…
Mathematics
Puzzles
Combinatorics
Graph Theory
Puzzles
counting
extremal graph theory
interview question
0
Undergraduate
By
Shiva Kintali
on Nov. 13, 2012 | Updated Jan. 16, 2017
Turing reducibility
Let \(A \leq_T B\) denote that language \(A\) is Turing reducible to language \(B\). Prove the following : Show that for any two languages \(A\) and \(B\) a language \(J\) exists, where …
Computer Science
Complexity Theory
turing reducibility
0
High School
By
Shiva Kintali
on Aug. 1, 2012 | Updated Jan. 16, 2017
Two Secret Integers
I am thinking of two integers, each of them is more than 1 and their sum is less than 100. I tell my friend A the sum of these two numbers, and another friend B, product of these two numbers. Then the…
Puzzles
Puzzles
math puzzle
0
High School
By
Shiva Kintali
on June 28, 2012 | Updated Jan. 16, 2017
Integral Rectangles
A large rectangle is partitioned into smaller rectangles, each of which has either integer height or integer width or both. Prove that the large rectangle also has this property.
Mathematics
Puzzles
Geometry
Puzzles
interview question
math puzzle
0
Graduate
By
Shiva Kintali
on Aug. 8, 2012 | Updated Jan. 16, 2017
Gallai Identities
Consider the following parameters of an undirected graph \(G\) on \(n\) vertices. \(\nu(G)\) is the size of a maximum matching of \(G\). \(\tau(G)\) is the size of a minimum vertex cover of \(G\). …
Mathematics
Graph Theory
edge cover
independent set
matching
vertex cover
0
Graduate
By
Shiva Kintali
on Aug. 29, 2012 | Updated Jan. 16, 2017
Random Intervals
There are \(n\) points on a line. These points are paired up at random to form \(n/2\) intervals. Prove that the probability that among these intervals there is one which intersects all the others i…
Mathematics
Puzzles
Probability
Puzzles
counting
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