   SEARCH HOME Math Central Quandaries & 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. tks Safdar Safdar,

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.

Janice

Safdar wrote back

Dear Janice,

AFTER 5 GAMESEACH PLAYER HAS $128. TKS N BST RGRDS SAFDAR Safdar, 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.

Harley     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.