MathDB

A particular country has seven distinct cities, conveniently named

C_1,C_2,\dots,C_7.

Between each pair of cities, a direction is chosen, and a one-way road is constructed in that direction connecting the two cities. After the construction is complete, it is found that any city is reachable from any other city, that is, for distinct

1 \leq i, j \leq 7,

there is a path of one-way roads leading from

C_i

C_j.

Compute the number of ways the roads could have been configured. Pictured on the following page are the possible configurations possible in a country with three cities, if every city is reachable from every other city. [Insert Diagram] Proposed by Ezra Erives

Problem Statement