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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. There are five men - A, B, C, D and E, six women P, Q, R, S, T and Z. A, B, and R are advocates. S, Q, P, D and C are doctors and the rest are teachers. A team has to be selected from these eleven persons subject to the following conditions:
    (I) A, P and Z have to be together.
    (II) B cannot go with D or R.
    (III) E and Q have to be together.
    (IV) C and T have to be together.
    (V) D and P cannot go together.
    (VI) C cannot go with Q.
    If the team formed consists of two male advocates, two lady doctors and one teacher, the members of the team can be:
  2. Seven boxes S, F, G, H, T and U are kept one over the other but not necessarily in the same order. Only two boxes are kept below S. Only one box is kept above U. Only one box is kept between U and B. G is kept immediately above F. T is kept at some place below H.
    How many boxes are kept between H and G?
  3. Seven boxes E, F, G, H, S, T and U are kept one over the other but not necessarily in themsame order. No box is kept above E. Only three boxes are kept between E and U. Only one box is kept between G and H. H is kept immediately above U. Only four boxes are kept between G and F. T is kept at some place above S. Which box is kept second below T?
  4. Seven boxes E, F, G, H, S, T and U are kept one over the other but not necessarily in the same order. H is kept immediately above E. T is kept immediately above U. Only F is kept above S. Only two boxes are kept above H. T is not kept at third position from the bottom.
    How many boxes are kept between G and F?
  5. Seven boxes A, B, C, D, E, F and G are kept one over the other but not necessarily in the same order.
    Only two boxes are kept between D and E. Only F is kept above C. No box is kept below E. G is kept at some place below A but at some place above B.
    How many boxes are kept below B?
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