Bridge, Algorithms, Math etc.

 Here is a cute problem for IOQM. What is the smallest $n$ such that $1^4, 2^4, \dots , 14^4$ all leave distinct remainders when divided by ...

 UPSC is India's civil services exam, and surprisingly, the following cute problem appeared. Admittedly, it was a multiple choice questi...

 Here is a cute problem from Peter Winkler. The series below converges in the interval $[0,1)$ $$ x - x^2 + x^4 - x^8 + \dots + (-1)^n x^{2^...

 Seems like there is a new exam for qualification to the regional math olympiads in India now. It is called IMOQ and is a set of fill in the...

Given a positive integer $n$. Show that $$ n = \sum_{k} \left[\sqrt{\dfrac{n}{k}}\right]$$ where $k$ runs through the square free numbers, $...

 Let $a$ be the unique real number that satisfies $1=a+a^3$. Let $S$ be any non-empty finite subset of the powers of $a$, i.e. $S \subset\{a...

 Let $\varphi = \frac{1+\sqrt{5}}{2}$ be the golden ratio. For every positive integer $n \ge 2$, show that there is exactly one way to write...

 In the recently concluded Willingdon Swiss pairs tournament in Bombay, my partner from Seattle made a very nice defense. Arvind had opened ...

 A cute problem from reddit. You have $2n$ people standing in an infinite row at spots say $1,2,3,..,2n$ (one person at each spot). A scient...

 You permute each of the digits $0, 1,2, \dots, 9$ and write them in a single row. A) Show that no matter what the permutation, some 3 adjac...

 A cute problem from Peter Winkler's collection of math puzzles. $$ S = \{n! | 1 \leq n \le 100, n \in N\}$$ Can we remove a single elem...

 What is the volume of the region in $R^n$ defined as follows $$ V_n = \{(x_1,x_2, \dots, x_n) \in R^n | x_i \ge 0 \text{ and } \sum x_i \le...

A basketball player is practising free throws. Their current success rate (ratio of successful throws to total) is exactly 70% (or 0.7 in te...

 Can the product of three positive consecutive integers be a perfect square? Scroll down for a solution . Assume the three integers are $n-1...