Round-Robin Tournament Scoring Logic

CAT 1998 Slot 1 · QA · Medium · Logical Reasoning

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A, B, C, D, ..., X, Y, Z are the 26 players who participated in a tournament. Everyone played with every other player exactly once. A win scores 2 points, a draw scores 1 point and a loss scores 0 point. None of the matches ended in a draw. No two players scored the same score. At the end of the tournament, a ranking list is published which is in accordance with the alphabetical order. Then:

  1. A.

    M wins over N

  2. B.

    N wins over M

  3. C.

    M does not play with N

  4. D.

    None of these

Answer

A

Explanation

Since there are 26 players, each plays 25 matches. Total points per match =2= 2. Possible scores for a player range from 0 to 50 (in steps of 2). Since all 26 players have distinct scores, the scores must be 50,48,46,…,050, 48, 46, \dots, 0. Since ranking aligns with alphabetical order, A scores 50, B scores 48, C scores 46, ..., M scores more than N. Player A wins against everyone. Player B loses only to A and beats everyone else. In general, any player beats all players ranked below them. Thus, M wins over N.

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