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

2020 DMO Stage 1, 1.

[b]Q[/b] Let $p,q,r$ be non negative reals such that $pqr=1$. Find the maximum value for the expression $$\sum_{cyc} p[r^{4}+q^{4}-p^{4}-p]$$ [i]Proposed by Aritra12[/i]

2020 DMO Stage 1, 2.

[b]Q[/b] On a \(10 \times 10\) chess board whose colors of square are green and blue in an arbitrary way and we are simultaneously allowed to switch all the colors of all squares in any \((2 \times 2)\) and \((5\times 5)\) region. Can we transform any coloring of the board into one where all squares are blue ? Give a proper explanation of your answer. Note. that if a unit square is part of both the $2\times 2$ and $5\times 5$ region,then its color switched is twice(i.e switching is additive) [i]Proposed by Aritra12[/i]