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High School
By
Shiva Kintali
on April 1, 2014 | Updated Jan. 16, 2017
Designing two dice
You are given two blank dice i.e., all the sides of the dice are blank. You are allowed to write any integers on the sides of the dice. Only one integer on each side. Write the integers such that …
Puzzles
Puzzles
interview question
math puzzle
0
Undergraduate
By
123forman
on May 8, 2014 | Updated Jan. 16, 2017
Democratic distribution of wealth
A crew of 100 pirates have captured 100 laptops. The pirates are ranked 1 through 100, with pirate 100 being the pirate king. Captured booty is distributed as follows. The pirate king proposes a dis…
Mathematics
Discrete Mathematics
Game Theory
induction
0
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 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 May 21, 2013 | Updated Jan. 16, 2017
Covering complete graph with bipartite graphs
The union of graphs \(G_1, \dots, G_k\), written \(G_1 \cup \dots \cup G_k\), is the graph with vertex set \(V(G_1) \cup \dots \cup V(G_k)\) and edge set \(E(G_1) \cup \dots \cup E(G_k)\). Prove tha…
Mathematics
Graph Theory
bipartite graph
graph union
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 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 May 7, 2012 | Updated Jan. 16, 2017
Graph Isomorphism, BPP and RP
The Graph Isomorphism Problem is to determine whether two given graphs are isomorphic to each other. Prove that if Graph Isomorphism is in BPP then it is in RP.
Computer Science
Complexity Theory
graph isomorphism
0
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
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