What a Coincidence!

              A group of seven young men named Arun, Binoy, Chunder, Dev, Edward, Fakruddin and Govind were recently engaged in a game. They had agreed that whenever a player won a game he should double the money of each of the other players, in other words he was to give the players just as much money as they had already in their pockets.

           In all they played seven games and, strangely, each won a game in turn in the order in which their names are given. But what was even stranger was that when they had finished the game each of the seven young men had exactly the same amount, Rs. 32 in his pocket.

         Can you find out how much money each person had with him before they began the game?

Answer:   A simple general solution to this problem would be as follows; 

                Let’s assume there are number of players. Then the amount held by every player at the end will be m (2ᶰ), and the last winner must have held at the start m (n+1), the next m (2n+1), and the next m (4n + 1) and so on to the first player, who must have held m (2 n-1 n+ 1).

             Therefore, in this case, n+7

             And the amount held by every player at the end was 2⁷ quarter of a rupee pieces.

            Therefore, m =1       

       

Govind started with 8 quarter of a rupee pieces or Rs. 3.75.

Edwards started with 29 quarter of a rupee pieces or Rs. 7.25

Edward started with 29 quarter of a rupee pieces or Rs. 7.25

Dev started with 57 quarter of a rupee pieces or Rs14.25

Chunder started with 113 quarter of a rupee pieces or Rs. 28.25

Binoy started with 225 quarter of a rupee pieces or Rs. 56.25.

Arun started with 449 quarter of a rupee pieces or Rs. 112.25