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

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Found problems: 2

2005 Junior Tuymaada Olympiad, 1
In each cell of the table $ 3 \times 3 $ there is one of the numbers $1, 2$ and $3$. Dima counted the sum of the numbers in each row and in each column. What is the greatest number of different sums he could get?
table greatest combinatorics

2006 MOP Homework, 3
For positive integer $k$, let $p(k)$ denote the greatest odd divisor of $k$. Prove that for every positive integer $n$, $$\frac{2n}{3} < \frac{p(1)}{1}+ \frac{p(2)}{2}+... +\frac{ p(n)}{n}<\frac{2(n + 1)}{3}$$
divisor inequalities odd greatest number theory mathematical induction parity