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MathNet 2012 Question 21

Math Olympiad Vault · MathNet 2012

Question 21

Marco, Fabrizio, and Giovanni, three mathematicians, challenge a group of four physicists to a table-football tournament. They play one match for every possible choice of two mathematicians (one attacking and one defending) against two physicists (one attacking and one defending). Every match lasts equally long, and the tournament takes $24$ hours without breaks. How long does Marco play in defence?

For example, Marco and Fabrizio play two different matches against a fixed physicist attacker and defender: one with Marco attacking and Fabrizio defending, and one with their roles reversed.

(A) $2$ hours $24$ minutes; (B) $4$ hours $48$ minutes; (C) $6$ hours; (D) $8$ hours; (E) $12$ hours.