Question: The minimum number of wins needed for a team in the first stage to guarantee its advancement to the next stage is
Explanation:
28 matches are played between 8 teams.
Consider option 1:
There is a possibility that 5 teams win exactly 5 matches each (5 × 5 = 25 matches played), one team wins 2 matches, one team wins exactly one match and one team lose all.
{For example: Let A, B, C, D, E, F, G, and H are the eight teams. A wins matches against B, C, D, E, F; B wins matches against C, D, E, F, G; C wins matches against D, E, F, G, H; G wins matches against A, D, E, F, H and H wins matches against A, B, D, E, F. Also E wins match against D. F wins matches against D and E. D loses all the matches}
Thus, for a team, there is no guarantee of its advancement to the next stage if it wins 5 matches.
But if a team wins six matches, there is no possibility that 5 teams will win 6 matches each. (As there are only 28 matches) Hence, the team will definitely advance to the next stage.
Hence, option (b).