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Subject: Late Friday Puzzle (Aug 19th) rss

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Harmonica
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Balthasar, Caspar and Melchior are on a long journey. After a long day travelling they put up the tent and find relaxation with a game. The loser of the game had to double the number of dollars of the others. After 5 games they have respectively 80, 90 and 100 dollars 8, 9 and 10 dollars.

What amount of dollars each had, when at the start of the first game?
 
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Billy McBoatface
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So we are to assume that the loser of each game always happened to have enough money to cover this doubling?

Can we assume that all players had integer dollar amounts at all times?
 
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Harmonica
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Coincidence happens in games, you know.
 
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Matt
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anemaat wrote:
Balthasar, Caspar and Melchior are on a long journey. After a long day travelling they put up the tent and find relaxation with a game. The loser of the game had to double the number of dollars of the others. After 5 games they have respectively 80, 90 and 100 dollars.

What amount of dollars each had, when at the start of the first game?


Spoiler (click to reveal)
You want to avoid anyone having an odd amount of money (in this case, ending in a '5'), so at the end of each round, we have:

Round 5: 80 90 100
Round 4: 40 180 50 (player 2 loses)
Round 3: 20 90 160 (3)
Round 2: 10 180 80 (2)
Round 1: 140 90 40 (1)
Start: 70 180 20 (2)


Unless I'm missing something... I guess the trick is that, in each round the loser from the previous round is not necessarily the one with the least money.

 
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Billy McBoatface
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I think it's pretty easy then...
Spoiler (click to reveal)

You can never have two players with odd scores after a game. So working backwords...
g5 -> 80/90/100
g4 -> 40/90+40+50=180/50
g3 -> 20/90/50+20+90=160
g2 -> 10/90+10+80=180/80
g1 -> 10+90+40=140/90/40
g0 -> 70/90+70+20=180/20

So they started with B=70, C=180, M=20. Games were lost by C, B, C, M, and C, in that order.

But I think there's a flaw...if they started with, for example, B=205, C=45, and M=20, and B lost the first game, then it would also work out. The rest of the games are the same as in my first answer.

Or perhaps they started with B=60, C=45, and M=125, then M lost the first game. Also works. Again, the rest of the games match the first answer.

So there are three possible answers.
 
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Harmonica
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I thought to be smart to add a '0' to each of the amounts .... Sorry!

Corrected the OP.
 
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John Breckenridge
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It depends on the fluctuating commodity prices of frankincense and myrrh.
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Harmonica
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... and above all ...
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