MathDB

In the country of Graphia there are

100

towns, each numbered from

1

100

. Some pairs of towns may be connected by a (direct) road and we call such pairs of towns adjacent. No two roads connect the same pair of towns.
Peter, a foreign tourist, plans to visit Graphia

100

times. For each

i

i=1,2,\dots, 100

, Peter starts his

i

-th trip by arriving in the town numbered

i

and then each following day Peter travels from the town he is currently in to an adjacent town with the lowest assigned number, assuming such that a town exists and that he hasn't visited it already on the

i

-th trip. Otherwise, Peter deems his

i

-th trip to be complete and returns home.
It turns out that after all

100

trips, Peter has visited each town in Graphia the same number of times. Find the largest possible number of roads in Graphia.

Problem Statement