Exercises
Multiple Choice
Articles
Open Problems
Login
14 items
Tagged:
pigeonhole principle
x
induction
x
Start over
- to expand, or dig in by adding more tags and revising the query.
Sort By:
trending ▼
date
2
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
0
Undergraduate
By
123forman
on May 8, 2014 | Updated Dec. 6, 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
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
Undergraduate
By
Shiva Kintali
on June 13, 2012 | Updated Dec. 6, 2017
Basics of Pigeonhole Principle
Prove the following : Given \(n\) integers, some nonempty subset of them has sum divisible by \(n\). Let \(A\) be a set of \(n+1\) integers from {\({1, 2,\dots , 2n}\)}. Prove that some element of \…
Mathematics
Discrete Mathematics
basics
counting
pigeonhole principle
1
Undergraduate
By
Shiva Kintali
on Sept. 30, 2013 | Updated Jan. 4, 2018
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…
Mathematics
Discrete Mathematics
counting
pigeonhole principle
0
Undergraduate
By
Shiva Kintali
on Sept. 29, 2013 | Updated Jan. 4, 2018
Fibonacci numbers and primes
The Fibonacci numbers are defined by \(F_1 = F_2 = 1\) and \(F_n = F_{n−1} + F_{n−2}\) for \(n \geq 3\). If \(p\) is a prime number, prove that at least one of the first \(p + 1\) Fibonacci numbers mu…
Mathematics
Combinatorics
fibonacci
pigeonhole principle
primes
0
High School
By
Shiva Kintali
on June 27, 2013 | Updated Jan. 4, 2018
Basics of Induction
Prove the following using induction: \(\sum_{i=1}^{n}{i} = \frac{n(n+1)}{2}\). \(\sum_{i=1}^{n}{i}^2 = \frac{n(n+1)(2n+1}{6}\). \(\sum_{i=1}^{n}{i}^3 = {(\frac{n(n+1)}{2})}^2\). …
Mathematics
Discrete Mathematics
induction
summation
1
Undergraduate
By
Shiva Kintali
on Sept. 27, 2013 | Updated Jan. 4, 2018
Fibonacci numbers and Induction
The Fibonacci numbers, \(F_0, F_1, F_2, \dots\) , are defined recursively by the equations \(F_0 = 0\), \(F_1 = 1\), and \(F_n = F_{n-1} + F_{n-2},\) for \(n > 1\). Prove that …
Mathematics
Discrete Mathematics
fibonacci
induction
tiling
0
High School
By
Shiva Kintali
on Sept. 30, 2013 | Updated Jan. 4, 2018
Using Binomial Theorem
Prove the following using binomial theorem and/or mathematical induction Let \(a\), \(b\) and \(n\) be natural numbers, prove that \(\frac{(a+\sqrt{b})^n + (a-\sqrt{b})^n}{2}\) is also a natural …
Mathematics
Discrete Mathematics
binomial theorem
induction
0
Undergraduate
By
Shiva Kintali
on June 16, 2012 | Updated Dec. 6, 2017
L shaped tiling
Consider a \(2^n × 2^n\) board with one (arbitrarily chosen) square removed, as in the following figure for \(n = 3\). Prove that any such board can be tiled (without gaps or overlaps) by \(L\)-shaped…
Puzzles
Puzzles
induction
tiling
1
2
next page »
icon
Sign In or Sign Up
icon
Invite Friends
Post Something
x
Select What You'd Like To Post
POST AN ARTICLE
POST AN OPEN PROBLEM
POST AN EXERCISE
POST A MULTIPLE-CHOICE QUESTION
Content Types
Articles
Open Problems
Exercises
Multiple-Choice Questions
Levels
High school
Undergraduate
Graduate
Subjects
Mathematics
Computer Science
Puzzles
Optimization
Trending tags
bipartite graph
matching
fibonacci
induction
tiling
math puzzle
jee
jee 2016
jee advanced
jee mathematics
Topics
Algebra
Algorithms
Approximation Algorithms
Calculus
Combinatorial Optimization
Combinatorics
Complexity Theory
Data Structures
Discrete Mathematics
Game Theory
Geometry
Graph Theory
Linear Algebra
Linear Programming
Logic
Mathematical Analysis
Mathematics
Matrix Theory
Number Theory
Optimization
Probability
Programming
Puzzles
Randomized Algorithms
Real Analysis
Trigonometry
×