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Bangladesh National Mathematical Olympiad 2016 Higher Secondary
Problem 5: Suppose there are

m

Martians and

n

Earthlings at an intergalactic peace conference. To ensure the Martians stay peaceful at the conference, we must make sure that no two Martians sit together, such that between any two Martians there is always at least one Earthling.
(a) Suppose all

m + n

Martians and Earthlings are seated in a line. How many ways can the Earthlings and Martians be seated in a line?
(b) Suppose now that the

m+n

Martians and Earthlings are seated around a circular round-table. How many ways can the Earthlings and Martians be seated around the round-table?

Problem Statement