



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


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