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Question

In a round-robin tournament, after each team has played exactly four matches, the number of wins/ losses of 6 participating teams are as follows
TeamWinLoss
A40
B04
C31
D22
E04
F31

Which of the two teams have certainly NOT played with each other?

The correct answer is
B and E

Tournament Match Analysis

In a round-robin tournament setting, the win/loss records provide crucial information about the matches played.

Consider the implications of a team having a record of 0 Wins and 4 Losses:

  • This signifies that the team lost every single match it participated in.
  • In this specific case, both Team B and Team E have records of 0 Wins and 4 Losses.

If two teams, say Team B and Team E, had played against each other:

  • One team would have had to win the match.
  • The other team would have had to lose the match.
  • This would result in the winning team having at least 1 win and the losing team having at least 1 loss.

Since both Team B and Team E have 0 wins recorded, it is impossible for them to have played each other. If they had met, the winner would have recorded a win, contradicting their zero-win status.

Therefore, Teams B and E must have played their four matches against other opponents (Teams A, C, D, and F).

Conclusion

Based on the win/loss records, the pair of teams that certainly have NOT played with each other is B and E.

This corresponds to Option D.

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Important Questions from Puzzle (Notes)

  1. Four individuals - P, Q, R and S - are suspects in a theft case. They make the following statements :
    P says: "Q is guilty."
    Q says: "R is guilty."
    R says: "P is innocent."
    S says: "I am innocent"
    If it is known that exactly one of them is guilty, and only the guilty person lies (all innocent people tell the truth), then who is the guilty one?
  2. In which company, C's interview was scheduled?
  3. Who went to Nagpur?
  4. What is the sum of the digits of the number Q?
  5. What is the sum of A and Q if A is smaller than B?
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