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 Bankim bid Lo? [This Question was asked as TITA]

• A. 3 rounds
• B. 2 rounds
• C. 4 rounds
• D. 5 rounds

Answer 1

The Correct Option is C

Bankim bid Lo in 4 rounds

Answer 2

Given:

1. Arun's score increased by 1 point from the third round to the sixth round.
2. Arun was the only player who bid Hi in exactly two out of the six rounds.
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.

We already established that:

• Arun bid Hi alone in the second round and the sixth round.
• Dipak bid Lo in the third round and Hi in either the first or second round.
  Now, let's determine Bankim's bids.

At the end of the third round, Bankim had -2 points, and at the end of the sixth round, Bankim had -1 point.
This means Bankim's score increased by 1 point from the third round to the sixth round.
To increase his score by 1 point, Bankim must have bid Hi in the fourth or fifth round and Lo in the other round.
Given that there are only two rounds left where Bankim could have bid Hi, and he must have bid Lo in the other rounds, Bankim must have bid Lo in the remaining four rounds.

So, Bankim bid Lo in 4 rounds.