CAT 2024 Slot 1 — DILR Question 9
Answer the following questions based on the information given below.
The game of QUIET is played between two teams. Six teams, numbered 1, 2, 3, 4, 5, and 6, play in a QUIET tournament. These teams are divided equally into two groups. In the tournament, each team plays every other team in the same group only once, and each team in the other group exactly twice. The tournament has several rounds, each of which consists of a few games. Every team plays exactly one game in each round.
The following additional facts are known about the schedule of games in the tournament.
1. Each team played against a team from the other group in Round 8.
2. In Round 4 and Round 7, the match-ups, that is the pair of teams playing against each other, were identical. In Round 5 and Round 8, the match-ups were identical.
3. Team 4 played Team 6 in both Round 1 and Round 2.
4. Team 1 played Team 5 ONLY once and that was in Round 2.
5. Team 3 played Team 4 in Round 3. Team 1 played Team 6 in Round 6.
6. In Round 8, Team 3 played Team 6, while Team 2 played Team 5.
How many rounds were there in the tournament?
Answer & solution
Answer: 8
Easy
Each team plays one game per round, so the number of rounds equals the number of games one team plays: its intra-group games plus its inter-group games.
Set-up. 6 teams split into two groups of 3. Within a group, each team plays the other two once; across groups, each team plays all three opponents twice. One game per team per round.
Games for one team. Two same-group opponents (once each) and three other-group opponents (twice each).
Rounds = games per team. Since every team plays exactly one game each round, the number of rounds is 8.