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High School
By
Shiva Kintali
on May 19, 2013 | Updated Dec. 6, 2017
Cutting Corners
Prove that removing opposite corner squares from an \(8 \times 8\) chessboard leaves a subboard that cannot be partitioned (tiled) into \(1 \times 2\) and \(2 \times 1\) rectangles. Prove the ab…
Mathematics
Puzzles
Graph Theory
Puzzles
interview question
tiling
0
High School
By
Shiva Kintali
on Sept. 28, 2013 | Updated Jan. 4, 2018
Limits sine cosine tangent
Evaluate the following limits : \(\lim_{x \to 0} {\frac{\sqrt{1+{\sin}^2x^2}-{\cos}^3x^2}{x^3{\tan}x}}\)
Mathematics
Calculus
cosine
limits
sine
tangent
0
High School
By
Shiva Kintali
on May 5, 2014 | Updated Jan. 4, 2018
Wine and water mixing problem
In the wine and water mixing problem, one starts with two barrels, one holding wine and the other an equal volume of water. A cup of wine is taken from the wine barrel and added to the water. A cup of…
Puzzles
Puzzles
math puzzle
0
High School
By
neeldhara
on June 7, 2012 | Updated Dec. 6, 2017
An Odd Party
\(N\) people are at a party. Every pair of guests has an odd number of common friends. Show that \(N\) is odd.
Mathematics
Puzzles
Combinatorics
Puzzles
counting
0
High School
By
Shiva Kintali
on March 24, 2013 | Updated Dec. 6, 2017
Infinite number of special primes
Prove that there are infinitely many primes of the form \(4n-1\) and \(4n+1\).
Mathematics
Number Theory
primes
0
High School
By
True IMO
on Oct. 9, 2012 | Updated Jan. 4, 2018
International Mathematical Olympiad 1998 Problem 3
For any positive integer \(n\), let \(d(n)\) denote the number of positive divisors of \(n\) (including \(1\) and \(n\) itself). Determine all positive integers \(k\) such that \(d(n^2)/d(n) = k\) for…
Mathematics
Number Theory
divisibility
imo
imo 1998
0
High School
By
Shiva Kintali
on Nov. 28, 2012 | Updated Dec. 6, 2017
Infinite series
Prove the following : \(\sum_{n=1}^{\infty}{\frac{1}{(2n-1)(2n+1)}} = \frac{1}{2}\)
Mathematics
infinite series
0
High School
By
Shiva Kintali
on Sept. 27, 2013 | Updated Jan. 4, 2018
Color of the last ball
In a large urn there are \(w\) white balls and \(b\) black balls. Beside the urn is a big pile (infinite number) of black balls. Now, we do the following. First, two balls are drawn at random from the…
Puzzles
Puzzles
invariant
0
High School
By
Shiva Kintali
on May 7, 2014 | Updated Jan. 4, 2018
Overlapping hour and minute hands
At what times are the hour and minute hands of a clock are exactly on top of each other ? At what times are the minute and second hands of a clock are exactly on top of each other ?
Puzzles
Puzzles
math puzzle
0
High School
By
Shiva Kintali
on May 7, 2014 | Updated Jan. 4, 2018
Adding the Numbers 1 to 100
What is the sum of the integers from 1 to 100 ? Origin : See this anecdote.
Puzzles
Puzzles
math puzzle
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