Search found 3 matches
- Thu Aug 25, 2016 12:51 pm
- Forum: Number Theory
- Topic: India TST 2014
- Replies: 3
- Views: 3543
India TST 2014
Find all positive integers $x$, $y$ such that $x^{\ x + y}=y^ {3 x}$.
- Mon Apr 04, 2016 2:02 pm
- Forum: Geometry
- Topic: feet of perpendicular and midpoint
- Replies: 1
- Views: 2527
feet of perpendicular and midpoint
In any triangle ABC, P, Q, R are the feet of perpendiculars from a point S to the sides BC, CA, AB respectively. L, M, N, are the midpoints of these sides. Prove that (LP)(BC) + (MQ)(CA) + (NR)(AB) = 0
- Wed Mar 30, 2016 1:09 pm
- Forum: Secondary Level
- Topic: 2014-national
- Replies: 15
- Views: 11672
Re: 2014-national
Imagine such a chessboard. A knight placed at a black square will go to a white square on its next move and vice versa. So the maximum number of knights placed in the board will be the number of black or white squares, assuring that none attacks anyone. Assuming that the board starts with a black sq...