Question 61
Marco, Fabrizio, and Giovanni, three mathematicians, challenge four physicists to a table-football tournament consisting of some number of matches. The group scoring the greatest total number of goals wins.
In each match the physicists score $2$ goals more than in the preceding match, starting with $1$ goal in the first. The combined total of both groups is $330$ goals, and the mathematicians win. Determine the smallest possible goal margin.
(A) $1$ goal; (B) $2$ goals; (C) $24$ goals; (D) $42$ goals; (E) $48$ goals.
In each match the physicists score $2$ goals more than in the preceding match, starting with $1$ goal in the first. The combined total of both groups is $330$ goals, and the mathematicians win. Determine the smallest possible goal margin.
(A) $1$ goal; (B) $2$ goals; (C) $24$ goals; (D) $42$ goals; (E) $48$ goals.