(i) the first game was the only game where two students of the same class played against each other,
(ii) the students of Class 5 won more games than the students of Class 4, and
(iii) the boys won two games and the girls won one game.
The student who did not lose any game is __________.
Problem Setup
We have four students:
- Class 5: Rishi (Boy), Swathi (Girl)
- Class 4: Pavan (Boy), Tanvi (Girl)
Game Rules:
- 3 games played sequentially.
- The loser of a game is eliminated from further participation.
Observations:
- (i) Only the first game featured players from the same class.
- (ii) Class 5 students won more games than Class 4 students (implying 2 wins for Class 5, 1 win for Class 4).
- (iii) Boys won 2 games, Girls won 1 game.
Objective: Identify the student who did not lose any game.
Logical Deduction
There are 3 games and 3 losers. The student who did not lose any game must be the winner of the final game.
Step 1: Analyze Game 1 Pairings (Condition i)
Condition (i) states that only the first game had students from the same class. This means Game 2 and Game 3 must have students from different classes.
Therefore, Game 1 must be either:
- Rishi (Class 5) vs Swathi (Class 5)
- Pavan (Class 4) vs Tanvi (Class 4)
Step 2: Analyze Win Conditions (Conditions ii & iii)
Total Wins:
- Class 5 wins = 2
- Class 4 wins = 1
- Boys wins = 2
- Girls wins = 1
Step 3: Evaluate Scenarios
Scenario A: Game 1 is Class 5 vs Class 5
Assume Game 1 is Rishi (C5, B) vs Swathi (C5, G).
- Game 1: Rishi vs Swathi.
- Let Rishi win. Swathi loses (eliminated).
- Wins: C5=1, Boys=1. Remaining players: Rishi (C5, B), Pavan (C4, B), Tanvi (C4, G).
- Game 2: Must be different classes. Let's assume Rishi (C5, B) vs Pavan (C4, B).
- Let Rishi win. Pavan loses (eliminated).
- Wins: C5=1, Boys=1. Cumulative Wins: C5=2, C4=0, Boys=2, Girls=0.
- Remaining players: Rishi (C5, B), Tanvi (C4, G).
- Game 3: Must be different classes. Rishi (C5, B) vs Tanvi (C4, G).
- To satisfy the final win counts (C5=2, C4=1, Boys=2, Girls=1), Tanvi must win this game.
- Tanvi wins. Rishi loses (eliminated).
- Wins: C4=1, Girls=1.
Final Check for Scenario A:
- Total Wins: C5=2 (Rishi G1, G2), C4=1 (Tanvi G3), Boys=2 (Rishi G1, G2), Girls=1 (Tanvi G3). Conditions (ii) and (iii) are met.
- Class Pairings: G1 (C5 vs C5 - Same), G2 (C5 vs C4 - Different), G3 (C5 vs C4 - Different). Condition (i) is met.
- Losers: Swathi (G1), Pavan (G2), Rishi (G3).
- Undefeated Student: Tanvi.
This scenario fits all conditions.
Scenario B: Game 1 is Class 4 vs Class 4
Assume Game 1 is Pavan (C4, B) vs Tanvi (C4, G).
If Tanvi wins G1 (C4=1, G=1), players are Tanvi(C4,G), Rishi(C5,B), Swathi(C5,G). Game 2 could be Rishi vs Swathi (C5 vs C5). This violates condition (i) because Game 2 would also be same-class.
If Pavan wins G1 (C4=1, B=1), players are Pavan(C4,B), Rishi(C5,B), Swathi(C5,G). Game 2 could be Rishi vs Swathi (C5 vs C5). This also violates condition (i).
Therefore, Scenario B is impossible.
Conclusion
Based on the logical deduction, the only scenario fitting all conditions is Scenario A, where Tanvi wins the final game and does not lose any game.
Important Questions from Puzzles
The diagram below shows a river system consisting of 7 segments, marked P, Q, R, S, T, U, and V. It splits the land into 5 zones, marked Z1, Z2, Z3, Z4, and Z5. We need to connect these zones using the least number of bridges. Out of the following options, which one is correct?
Note: The figure shown is representative.
- A thin wire is used to construct all the edges of a cube of $1 \text{ m}$ side by bending, cutting and soldering the wire. If the wire is $12 \text{ m}$ long, what is the minimum number of cuts required to construct the wire frame to form the cube?
In the $4 \times 4$ array shown below, each cell of the first three columns has either a cross (X) or a number, as per the given rule.
1 1 2 2 X 3 2 X 4 1 2 X Rule: The number in a cell represents the count of crosses around its immediate neighboring cells (left, right, top, bottom, diagonals).
As per this rule, the maximum number of crosses possible in the empty column is
In the square grid shown on the left, a person standing at P2 position is required to move to P5 position.
The only movement allowed for a step involves, “two moves along one direction followed by one move in a perpendicular direction”. The permissible directions for movement are shown as dotted arrows in the right.
For example, a person at a given position Y can move only to the positions marked X on the right.
Without occupying any of the shaded squares at the end of each step, the minimum number of steps required to go from P2 to P5 is
In the 4 x 4 array shown below, each cell of the first three rows has either a cross (X) or a number.
1 X 4 3 X 5 5 4 3 X 6 X
The number in a cell represents the count of the immediate neighboring cells (left, right, top, bottom, diagonals) NOT having a cross (X). Given that the last row has no crosses (X), the sum of the four numbers to be filled in the last row is
