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High School
By
TrueShelf Inc.
on July 6, 2017
The Future Is Adaptive: An Interview with TrueShelf’s Shiva Kintali
To try TrueShelf mathematics learning platform, Click Here To check out our pricing model, Click Here As a teacher, mathematician and cyclist, TrueShelf CEO and founder Dr. Shiva Kintali …
Mathematics
Algebra
blog
0
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
2
High School
By
TrueShelf Inc.
on Nov. 14, 2016 | Updated July 2, 2017
International Mathematical Olympiad 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
1
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
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
0
High School
By
TrueShelf Inc.
on July 1, 2017 | Updated July 2, 2017
International Mathematical Olympiad 2015 Problem 2
Determine all triples of positive integers such that each of the numbers is a power of 2.
Mathematics
Algebra
imo
imo 2015
1
High School
By
TrueShelf Inc.
on July 21, 2016 | Updated July 2, 2017
International Mathematical Olympiad 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
imo
imo 2016
polygon
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
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
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