Question 99
Some of the cities in a country are connected by direct roads. Let $t$ be the smallest positive integer for which there is a city from which every other city can be reached by traveling along at most $t$ roads. Prove that there exist cities $A_1, A_2, \dots, A_{2t-1}$ such that for all $i \lt j$ with $i = 1, 2, \dots, 2t-2$ and $j = 2, 3, \dots, 2t-1$ the cities $A_i$ and $A_j$ are connected by a road if and only if $i + 1 = j$.