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.

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Found problems: 8

2004 Bulgaria Team Selection Test, 3
Tags: Ross Mathematics Program , induction , linear algebra , matrix , combinatorics proposed , combinatorics
In any cell of an $n \times n$ table a number is written such that all the rows are distinct. Prove that we can remove a column such that the rows in the new table are still distinct.

2012 Indonesia TST, 2
Tags: induction , Ross Mathematics Program , combinatorics proposed , combinatorics
An $m \times n$ chessboard where $m \le n$ has several black squares such that no two rows have the same pattern. Determine the largest integer $k$ such that we can always color $k$ columns red while still no two rows have the same pattern.

2004 Bulgaria Team Selection Test, 3
Tags: Ross Mathematics Program , induction , linear algebra , matrix , combinatorics proposed , combinatorics
In any cell of an $n \times n$ table a number is written such that all the rows are distinct. Prove that we can remove a column such that the rows in the new table are still distinct.

2006 MOP Homework, 4
Tags: geometry , parallelogram , Ross Mathematics Program , geometry unsolved
1.14. Let P and Q be interior points of triangle ABC such that \ACP = \BCQ and \CAP = \BAQ. Denote by D;E and F the feet of the perpendiculars from P to the lines BC, CA and AB, respectively. Prove that if \DEF = 90, then Q is the orthocenter of triangle BDF.

2005 Vietnam National Olympiad, 2
Tags: Ross Mathematics Program , number theory proposed , number theory
Find all triples of natural $ (x,y,n)$ satisfying the condition: \[ \frac {x! \plus{} y!}{n!} \equal{} 3^n \] Define $ 0! \equal{} 1$

2012 Indonesia TST, 2
Tags: induction , Ross Mathematics Program , combinatorics proposed , combinatorics
An $m \times n$ chessboard where $m \le n$ has several black squares such that no two rows have the same pattern. Determine the largest integer $k$ such that we can always color $k$ columns red while still no two rows have the same pattern.

2014 Regional Olympiad of Mexico Center Zone, 6
Tags: linear algebra , Ross Mathematics Program , combinatorics , graph theory
In a school there are $n$ classes and $n$ students. The students are enrolled in classes, such that no two of them have exactly the same classes. Prove that we can close a class in a such way that there still are no two of them which have exactly the same classes.

1964 Putnam, B6
Tags: Ross Mathematics Program , real analysis , real analysis unsolved
This is rather simple, but I liked it :). Show that a disk cannot be partitioned into two congruent subsets.