Solve the Game Theory Problem: How Many Players Started?

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Discussion Overview

The discussion revolves around a game theory problem involving multiple players who start with a certain amount of money and play a game with specific rules regarding payments and distribution of funds. The objective is to determine the initial number of players based on the game's outcome.

Discussion Character

  • Mathematical reasoning
  • Homework-related

Main Points Raised

  • One participant presents the problem and expresses uncertainty about how to prove the solution.
  • Another participant suggests that the problem can be approached using algebra and number theory, proposing to define the number of players as p and calculate the total initial amount of money and the money paid to the house.
  • A participant questions the reasoning behind the payment structure in the rounds, specifically how the payment changes in the (p-2)th round.
  • One participant claims to have found a solution through guess and check, suggesting that p=58, but seeks a more formal proof.
  • A later reply corrects the round number reference and suggests using the formula for the sum of consecutive natural numbers to aid in the proof.

Areas of Agreement / Disagreement

The discussion contains multiple viewpoints on how to approach the problem, with no consensus on a definitive solution or method of proof. Participants express uncertainty and seek clarification on specific aspects of the problem.

Contextual Notes

Participants have not fully resolved the mathematical steps necessary to prove the solution, and there are unresolved assumptions regarding the game mechanics and their implications on the final amounts.

galois427
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i need help with solving tihs problem. I'm not really sure how to prove it.

several people started with $300 each, and played a game with the following strange rules. each player pays $10 to the house at the beginning of each round. during each round, one active player is declared the loser, and he distributes all of his money in equal amounts to the remaining players. the loser must then leave, but all of the other players go on to the next round. the game is over when only one player remains. at the end of the game, the surviving olayer was surprised to discover that he had exactly $300, equaling his starting amount. how many players were there at the beginning?
 
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This looks more like an algebra/number theory problem to me...

Assume there are p players.

The total initial amount of money is 300p

The money going to the house is as follows :

1st round : 10p
2nd round : 10(p-1)
3rd round : 10(p-2)
.
.
(p-2)th round : 20

Sum these to find the total money given to the house.

The difference is what the winner has.

You have a simple quadratic equation in p. Solve it.
 
can you explain that a little more. how does (p-2)th round : 20?
i found out, by guess and check, that p=58, but how do you go about proving it?
 
Last edited:
nvm, i just figured it out. thanks.
 
galois427 said:
can you explain that a little more. how does (p-2)th round : 20?
i found out, by guess and check, that p=58, but how do you go about proving it?

Oops, sorry. The last round should be the (p-1)th round. :redface:

Use the formula for the sum of p consecutive natural numbers.
 

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