Here are problems from Junior Balkan MO 2007:

1 | Let be positive real number such that . Prove that the equation has no real solution. | S |

2 | Let be a convex quadrilateral with , and . The diagonals and intersect at point . Determine the measure of . | S |

3 | Given are points in the plane, no three of them belonging to a same line. Each of these points is colored using one of four given colors. Prove that there is a color and at least scalene triangles with vertices of that color. | S |

4 | Prove that if is a prime number, then is not a perfect square. |

These are not very hard, but it took me 2 hours to solve 3. one, cuz I`m not very good at analysis.

Here are solutions to all of them(click on here :)).

## No comments:

Post a Comment