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High School
By
True IMO
on Nov. 14, 2016 | Updated Jan. 4, 2018
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 p…
Mathematics
Combinatorics
imo
imo 2016
polynomials
0
High School
By
Shiva Kintali
on May 19, 2013 | Updated Dec. 6, 2017
Basics of counting
Let \(S = {1,2,...,n}\). How many ordered pairs \((A,B)\) of subsets of \(S\) are there that satisfy \(A \subseteq B\) ?
Mathematics
Combinatorics
basics
counting
0
High School
By
Shiva Kintali
on Sept. 27, 2013 | Updated Jan. 4, 2018
Binomial coefficients
Evaluate the following sums using combinatorial methods and algebraic methods : \(\displaystyle \sum_{i=0}^{k} {m \choose i}{n \choose k-i}\) \(\displaystyle \sum_{i=0}^{n} {n \choose i}^2\) …
Mathematics
Combinatorics
binomial theorem
counting
n choose k
0
High School
By
Shiva Kintali
on Sept. 28, 2013 | Updated Jan. 4, 2018
Bijective counting
Let \(S = {1,2,...,n}\). How many ordered pairs \((A,B)\) of subsets of \(S\) are there that satisfy \(A \subseteq B\) ? Let \(S = {1,2,...,n}\). How many ordered pairs \((A,B)\) of subsets of …
Mathematics
Combinatorics
bijection
counting
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
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Combinatorics
Puzzles
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