Math Problem Statement
A, B, C, and D play dice games where the loser doubles the amount of money of all other players. Four games are played in all, and A, B, C, and D lose these games in this sequence only. Each player has Rs. 96 at the end of the fourth game. What is the amount with C at the end of the third game?
Solution
Let's solve the problem step by step.
Understanding the Problem
- Initial Condition: All players have an equal amount of money initially. Let's denote this amount by .
- Game Rules:
- The loser doubles the amount of money of all other players.
- Four games are played, and the losers are A, B, C, and D, respectively.
- Final Condition: Each player has Rs. 96 at the end of the fourth game.
Step-by-Step Calculation
After Game 1:
- Loser: A
- Other Players' Money Doubles:
- If A loses, B, C, and D's money doubles.
- Equations: A's money is after doubling others' money, but A had to match the others' gain, so A would end up with the same amount as each other player.
So after the first game, the amount with each player will be:
After Game 2:
- Loser: B
- Other Players' Money Doubles:
- A, C, and D’s money doubles.
- Equations:
After Game 3:
- Loser: C
- Other Players' Money Doubles:
- A, B, and D’s money doubles.
- Equations:
After Game 4:
- Loser: D
- Other Players' Money Doubles:
- A, B, and C’s money doubles.
- Equations:
Given that after the fourth game, each player has Rs. 96:
Calculation of Amount with C After the Third Game
After the third game, the amount with C was:
Thus, after the third game, C had Rs. 3.
Answer:
The amount with C at the end of the third game was Rs. 3.
Would you like more details on this solution, or do you have any questions?
Related Questions:
- What was the amount with B at the end of the second game?
- How much money did D have after losing the second game?
- What was the initial amount each player had before the games started?
- How much money did each player have after the first game?
- What would have been the result if B lost the first game instead of A?
Tip: To solve problems involving sequential changes like this, always track the changes step by step for each participant after every round or event.
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Math Problem Analysis
Mathematical Concepts
Arithmetic
Game Theory
Equations
Formulas
Doubling principle
Theorems
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Suitable Grade Level
Grades 7-9
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