Question

Hree people play a game in which one person loses and two people win each round. The loser must pay each winner the amount that the winner already has. The players agree to play three rounds. At the end of the three rounds, each player has lost one round and has $8. How much money did each player have at the start

Answer 1

$7 ; $4 ; $3

Explanation:

Given that:

1 player loses and 2 wins

Loser pays each winner amount each winner already has

3 rounds was played

At the end, each player has lost 1 round each and has $8.00

Since each player lost 1 round each, then each player won twice.

Given that the players are A, B and C

Starting from the last round :

Recall; they all have $8 after the last round.

If A lost the last round and pays B and C the amount they already have.

B and C finally have $8, Hence amount A paid B and C = 8/2 = $4 each

Hence, at the end of 2nd round / before last round :

A has ($8 paid + $8 final) = $16

B and C each have $4

End of first round before 2nd round of game:

If B lost, and pays A and C the amount they already have ;

A finally has 16 hence, amount B pays A = 16/2 = $8

Amount B pays C = 4/2 = $2

A = $8

B = $4 + $(8 + 2) = $14

C = $2

Ist round

C will lose :

Amount C pays B = $14 / 2 = $7

Amount C pays A = $8 /2 = $4

Hence, amount C has before round 1:

$7 + $4 + $2 = $13

Hence; Before the game ;

Either of the three players have ;

$7 ; $4 and $13