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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
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
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
Graduate
By
domotorp
on June 6, 2012 | Updated Dec. 6, 2017
Read Once Promised Majority
Suppose the input is \(n\) numbers from \(1\) to \(n\), separated by commas and we know that one of the number occurs more than \(n/2\) times. How can we decide which if we can read the input tape onl…
Computer Science
Puzzles
Complexity Theory
Puzzles
read once
0
High School
By
Shiva Kintali
on April 1, 2014 | Updated Dec. 6, 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
High School
By
Shiva Kintali
on Aug. 20, 2013 | Updated Jan. 4, 2018
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
High School
By
Shiva Kintali
on May 7, 2014 | Updated Jan. 4, 2018
Sock Drawer puzzle
There are 10 socks of each of the following colors in a drawer: red blue green black white i.e., there are 50 socks. The socks are arbitrarily distributed in the drawer. You are blind-f…
Puzzles
Puzzles
math puzzle
pigeonhole principle
0
Graduate
By
Shiva Kintali
on Aug. 29, 2012 | Updated Dec. 6, 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
0
Undergraduate
By
Shiva Kintali
on May 31, 2012 | Updated Dec. 6, 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
High School
By
Shiva Kintali
on June 28, 2012 | Updated Dec. 6, 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
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