5

Part of 2005 China National Olympiad

Problems(1)

minimum number of triangles with the area not more than 1/4

Source: china mathematical olympiad cmo 2005 final round - Problem 5

There are 5 points in a rectangle (including its boundary) with area 1, no three of them are in the same line. Find the minimum number of triangles with the area not more than

\frac 1{4}

, vertex of which are three of the five points.

geometryrectanglecombinatorial geometrycombinatorics unsolvedcombinatorics