Question

Three girls play three rounds of a game. On each round there are two winners and one loser. The girl who loses on a round has to double the number of chips that each of the other girls has by giving up some of her own chips. Each girl loses one round. At the end of three rounds, each girl has 24 chips. How many chips did each girl have at the beginning of the game?

Answer 1

The Solution:

Let the 3 girls be represented with A, B, and C.

At round 1:

Let C be the loser while A and B are winners.

A has 12 chips

B has 21 chips

C has 39 chips

At round 2:

Let B be the loser while A and C are winners.

A has 24 chips

B has 42 chips

C has 6 chips

At round 3:

Let A be the loser while A and C are winners.

A has 24 chips.

B has 24 chips.

C has 24 chips.

Therefore, the girl A has 12 chips, girl B has 21 chips and girl C has 39 chips at the beginning of the game.