Question

The Hi-Lo game is a four-player game played in six rounds. In every round, each player chooses to bid Hi or Lo. The bids are made simultaneously. If all four bid Hi, then all four lose 1 point each. If three players bid Hi and one bids Lo, then the players bidding Hi gain 1 point each and the player bidding Lo loses 3 points. If two players bid Hi and two bid Lo, then the players bidding Hi gain 2 points each and the players bidding Lo lose 2 points each. If one player bids Hi and three bid Lo, then the player bidding Hi gains 3 points and the players bidding Lo lose 1 point each. If all four bid Lo, then all four gain 1 point each.
Four players Arun, Bankim, Charu, and Dipak played the Hi-Lo game. The following facts are known about their game:
1.At the end of three rounds, Arun had scored 6 points, Dipak had scored 2 points, Bankim and Charu had scored -2 points each.
2.At the end of six rounds, Arun had scored 7 points, Bankim and Dipak had scored -1 point each, and Charu had scored -5 points.
3.Dipak’s score in the third round was less than his score in the first round but was more than his score in the second round.
4.In exactly two out of the six rounds, Arun was the only player who bid Hi.
In how many rounds did all four players make identical bids?[This Question was asked as TITA]

• A. 5 rounds
• B. 3 rounds
• C. 1 rounds
• D. 2 rounds

Answer 1

The Correct Option is D

Provided Information:

1. After three rounds, scores were: Arun (6), Dipak (2), Bankim (-2), Charu (-2).
2. After six rounds, scores were: Arun (7), Bankim (-1), Dipak (-1), Charu (-5).
3. Dipak's third-round score was between his first-round and second-round scores.
4. Arun was the sole Hi bidder in exactly two of the six rounds.

Analysis:

• Arun's score increased by 1 point from round 3 to round 6 (7 - 6 = 1). This suggests that the sixth round was one of the two rounds where he bid Hi alone.
• When Arun bid Hi alone, he lost 1 point. If the sixth round was one such instance, the other instance could be round 2, 3, or 4.

Assumption: Arun bid Hi alone in rounds 2 and 6.

• If Arun bid Hi alone in round 2, and his score after round 3 was 6, his score after round 2 was 6 - 3 = 3.
• Dipak's third-round score was between his first and second. His score after round 3 was 2. This implies his score after round 1 was 2 - 3 = -1. His score after round 2 was -1 + 3 = 2. This means Dipak bid Hi in round 1 and Lo in rounds 2 and 3.
• Bankim and Charu's scores after round 3 were -2. This implies they bid Hi in round 1 and Lo in rounds 2 and 3.

Analysis of Bankim and Dipak's scores after round 6:

• Bankim and Dipak both had a score of -1 after round 6. For their scores to be equal, Bankim must have bid Hi in round 4, and Dipak must have bid Lo in round 4.

Conclusion on bids:

Bankim and Dipak both bid Hi in round 1 and Lo in rounds 2 and 4.

Rounds with identical bids:

• Round 1: All four players bid Hi.
• Rounds 2 and 4: All four players bid Lo.

All four players made identical bids in 2 rounds.

Result: 2 rounds.