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High School
By
TrueShelf Inc.
on Aug. 28, 2013 | Updated Jan. 16, 2017
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
TrueShelf Inc.
on Nov. 14, 2016 | Updated Feb. 24, 2017
IMO 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
Shiva Kintali
on June 24, 2012 | Updated Jan. 16, 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
1
High School
By
TrueShelf Inc.
on July 21, 2016 | Updated Jan. 16, 2017
IMO 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
polygon
0
Undergraduate
By
TrueShelf Inc.
on May 21, 2014 | Updated Jan. 16, 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 Jan. 16, 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
High School
By
TrueShelf Inc.
on Oct. 21, 2014 | Updated Jan. 16, 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
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 May 7, 2014 | Updated Jan. 16, 2017
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-folded. …
Puzzles
Puzzles
math puzzle
pigeonhole principle
0
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
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