3
Part of 2007 Pan African
Problems(2)
Make a round-trip of length not divisible by 3
Source: PAMO 2007 Q3
12/10/2013
In a country, towns are connected by roads. Each town is directly connected to exactly three other towns. Show that there exists a town from which you can make a round-trip, without using the same road more than once, and for which the number of roads used is not divisible by . (Not all towns need to be visited.)
geometry3D geometrycombinatorics unsolvedcombinatorics
Greatest area made by perpendiculars through centroid
Source: PAMO 2007 Q6
12/10/2013
An equilateral triangle of side length 2 is divided into four pieces by two perpendicular lines that intersect in the centroid of the triangle. What is the maximum possible area of a piece?
geometrygeometry unsolved