MathDB

In the fictional country of Mahishmati, there are

50

cities, including a capital city. Some pairs of cities are connected by two-way flights. Given a city

A

, an ordered list of cities

C_1,\ldots, C_{50}

is called an antitour from

A

if
[*] every city (including

A

) appears in the list exactly once, and [*] for each

k\in \{1,2,\ldots, 50\}

, it is impossible to go from

A

C_k

by a sequence of exactly

k

(not necessarily distinct) flights.
Baahubali notices that there is an antitour from

A

for any city

A

. Further, he can take a sequence of flights, starting from the capital and passing through each city exactly once. Find the least possible total number of antitours from the capital city.
Proposed by Sutanay Bhattacharya

Problem Statement