MathDB

In the space are given

2006

distinct points, such that no

4

of them are coplanar. One draws a segment between each pair of points. A natural number

m

is called good if one can put on each of these segments a positive integer not larger than

m

, so that every triangle whose three vertices are among the given points has the property that two of this triangle's sides have equal numbers put on, while the third has a larger number put on. Find the minimum value of a good number

m

Problem Statement