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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.

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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.

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

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