Math CentralQuandaries & Queries


Dear sir,

pls answer for following questn:

five players agreed that after every game, the loser doubles every body's money. they played 5 games and everybody lost once. after the 5 games, everybody had 4128. How much money did each of the players have before the game?
show your work.




After 5 games does each player have 4128 or is it the combined amount of money between all 5 players? My suggestion would be to be to try to work backwards in the problem.


Safdar wrote back

Dear Janice,





The suggestion by Janice that you try working backwards is an excellent strategy. Suppose I number the players, player1, player 2 and so on and that player 1 lost the first game, player 2 lost the second game up to the fifth game that player 5 lost. I am going to use a table to keep track of the amount of money each player has. After the fifth game my table is

Player 1 Player 2 Player 3 Player 4 Player 5
$128 $128 $128 $128 $128

Player 5 lost the fifth game and doubled each other player's money so players 1 to 4 had $64 at the beginning of the fifth game. Player 5 gave each of them $64 so he gave a total of 4 × $64 = $256 and hence at the beginning of the fifth game he had $256 + $128 = $384. Thus my table after the fourth game is

Player 1 Player 2 Player 3 Player 4 Player 5
$128 $128 $128 $128 $128
$64 $64 $64 $64 $384

Player 4 lost the fourth game and doubled the other player's money so at the beginning of the fourth game the table is

Player 1 Player 2 Player 3 Player 4 Player 5
$128 $128 $128 $128 $128
$64 $64 $64 $64 $384
$32 $32 $32 $???? $192

How much money did player 4 have before the fourth game?

Continue the table back to the beginning of the five games.

Notice that there is a check on your arithmetic. After the last game the players have a total of 5 × $128 = $640. Each game just moves the money around so the sum of each row in the table must be $640.


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