MathDB

There are two airlines A and B and finitely many airports. For each pair of airports, there is exactly one airline among A and B whose flights operates in both directions. Each airline plans to develop world travel packages which pass each airport exactly once using only its flights. Let

a

and

b

be the number of possible packages which belongs to A and B respectively. Prove that

a-b

is a multiple of

4

.
The official statement of the problem has been changed. The above is the form which appeared during the contest. Now the condition 'the number of airports is no less than 4'is attached. Cite the following link. https://artofproblemsolving.com/community/c6h2923697p26140823

Problem Statement