MathDB

2

Part of 2007 Mexico National Olympiad

Problems(2)

<APB = < BPC Locus

Source: OMM 2007 2

7/19/2014
Given an equilateral △ABC\triangle ABC, find the locus of points PP such that ∠APB=∠BPC\angle APB=\angle BPC.
trigonometrygeometrycircumcircleangle bisectorgeometry unsolved
Lightning Bugs

Source: OMM 2007 5

7/19/2014
In each square of a 6×66\times6 grid there is a lightning bug on or off. One move is to choose three consecutive squares, either horizontal or vertical, and change the lightning bugs in those 33 squares from off to on or from on to off. Show if at the beginning there is one lighting bug on and the rest of them off, it is not possible to make some moves so that at the end they are all turned off.
combinatorics unsolvedcombinatorics