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 Dipak gain exactly 1 point? [This Question was asked as TITA]

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

Answer 1

The Correct Option is A

To address the issue, we must examine the provided data and trace score fluctuations across game rounds, adhering to the Hi-Lo game mechanics and presented statements. The subsequent steps will be followed:

• Score Change Dynamics: According to game regulations:
  • All participants lose 1 point if all bid Hi.
  • If three bid Hi and one bids Lo, the three gain 1 point each, and the single Lo bidder loses 3 points.
  • When two bid Hi and two bid Lo, the Hi bidders earn 2 points each, while the Lo bidders lose 2 points each.
  • A single Hi bidder and three Lo bidders result in the Hi bidder gaining 3 points and the Lo bidders losing 1 point each.
  • All participants gain 1 point if all bid Lo.
• Starting Scores: Post-round 3 scores: Arun: 6, Dipak: 2, Bankim: -2, Charu: -2.
• Concluding Scores: Post-round 6 scores: Arun: 7, Dipak: -1, Bankim: -1, Charu: -5.
• Score Shifts (Rounds 4-6):
  
  • Arun (6 to 7, +1): A net gain of 1 point implies Arun bid Lo in all rounds during this period.
  • Bankim (-2 to -1, +1): A gain of 1 point.
  • Dipak (2 to -1, -3): A net loss of 3 points.
  • Charu (-2 to -5, -3): A consistent point decrease.
• Dipak's Score Progression:
  1. Dipak's total score change from round 4 to 6 is -3 (from 2 to -1).
  2. Within these rounds, Dipak must have achieved a +1 score in one instance.
• Fact Verification:
  1. Fact 3: Dipak's round 3 score (2) falls between his scores from rounds 1 and 2.
  2. Based on possible scoring scenarios, Dipak must have scored +1 exactly once to reconcile the given score range and the overall decrease.
  3. Fact 4: Arun was the sole Hi bidder in precisely two rounds. Rounds 3 and 6 are potential matches for this condition.

Consequently, based on the analysis and stipulated conditions, Dipak achieved a gain of exactly 1 point in 1 round. This outcome validates the conclusion.