# Loser-Winner-Loser

3 players start a game in which one of the players wins and the other 2 lose.

Each loser has to pay the winner twice the amount he (the winner) had when (each) game started.

After 3 consecutive games, each has won once.

This is how much each player has (after those 3 games):

Player #1:  $20 Player #2:$118

Player #3:  $27  Question: Which players lost money and how much? (In relation to how much they had, before the first game) Note: The smallest monetary unit is$1 (i.e., no fractions) and the money has to be paid immediately after each game.

If each player pays the winner twice the amount of money he already had, then he has five times his original amount of money.

The only person whose money is a multiple of five after the third round is Player 1, so he must have won the third round. The winnings before the third round were as follows:

    Player 1:   $4 Player 2:$126
Player 3:  $35  Now, Player 3 is the one with a multiple of 5, so he was the winner the second round:  Player 1:$18
Player 2: $140 Player 3:$7


And now, Player 2 is the one with a multiple of 5, so he was the winner the first round:

    Player 1: $74 Player 2:$28
Player 3: \$63


Those are the amounts they started with.

• Congrats! And +1 for speed! – logicean Jun 3 '15 at 3:15