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: 127

2005 Bosnia and Herzegovina Junior BMO TST, 1
Non-negative real numbers $x, y, z$ satisfy the following relations: $3x + 5y + 7z = 10$ and $x + 2y + 5z = 6$. Find the minimum and maximum of $w = 2x - 3y + 4z$.
inequalities min max algebra

2016 Saint Petersburg Mathematical Olympiad, 2
The rook, standing on the surface of the checkered cube, beats the cells, located in the same row as well as on the continuations of this series through one or even several edges. (The picture shows an example for a $4 \times 4 \times 4$ cube,visible cells that some beat the rook, shaded gray.) What is the largest number do not beat each other rooks can be placed on the surface of the cube $50 \times 50 \times 50$?
3-dimensional geometry cube geometry 3d geometry max combinatorics combinatorial geometry solid geometry