This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

Tags were heavily modified to better represent problems.

AND
OR
NO

Found problems: 2

2020 Bundeswettbewerb Mathematik, 4
In each cell of a table with $m$ rows and $n$ columns, where $m<n$, we put a non-negative real number such that each column contains at least one positive number. Show that there is a cell with a positive number such that the sum of the numbers in its row is larger than the sum of the numbers in its column.
nonnegative inequalities combinatorics sum algebra bijection

2011 Bosnia and Herzegovina Junior BMO TST, 2
Prove inequality, with $a$ and $b$ nonnegative real numbers: $\frac{a+b}{1+a+b}\leq \frac{a}{1+a} + \frac{b}{1+b} \leq \frac{2(a+b)}{2+a+b}$
nonnegative inequalities inequality algebra