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High School
By
TrueShelf Inc.
on May 27, 2014 | Updated Jan. 16, 2017
JEE-Main 2013 Mathematics 31
The circle passing through \((1, −2)\) and touching the axis of \(x\) at \((3, 0)\) also passes through the point
Mathematics
Geometry
circle
jee
jee main
0
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
0
Undergraduate
By
TrueShelf Inc.
on June 13, 2013 | Updated Jan. 16, 2017
Among the following sorting algorithms, which one has the least worst-case running time asymptotically ?
Computer Science
Algorithms
sorting
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
High School
By
TrueShelf Inc.
on May 29, 2014 | Updated Jan. 16, 2017
JEE-Main 2013 Mathematics 35
All the students of a class performed poorly in Mathematics. The teacher decided to give grace marks of 10 to each of the students. Which of the following statistical measures will not change even aft…
Mathematics
jee
jee main
statistics
variance
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3
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