MathDB

Let

n>2

be an integer. In a country there are

n

cities and every two of them are connected by a direct road. Each road is assigned an integer from the set

\{1, 2,\ldots ,m\}

(different roads may be assigned the same number). The priority of a city is the sum of the numbers assigned to roads which lead to it. Find the smallest

m

for which it is possible that all cities have a different priority.

Problem Statement