Someone began with 50 cents

Algebra Level 3

Anna, Brenda, and Cynthia are taking turns playing a two-person game. Each game, the player with the least amount of money bets it all, and the opponent calls it. The results of the games are as follows:

  • Anna and Brenda play the first game. Anna wins and thereby doubles her money.
  • Brenda and Cynthia play the second game. Brenda wins and doubles her money.
  • Anna and Cynthia play the third game. Cynthia wins and doubles her money.

All three of them end up with equal amounts of money.

They each started with an integer number of cents. One of the players started with 50 cents—who was it?


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