Thread: Twelve coins problem
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Old 06-14-2010, 08:01 PM   #8
obs20
Wizard
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Okay here it goes:
Spoiler:

We need 9 good coins and 2 coins to pay the skinflint for the scale. We shouldn't get upset to offer him 3 coins of which 2 are good. Let him figure it out himself.

Put 3 coins on the left side of the scale.
Put 3 coins on the right side of the scale.
If the scale balances great we know that we have 6 good coins.
Then
Take 3 coins off the left side and replace them with 3 of the remaining coins.
If the scale balances great we have 9 good coins.
If not we know that the 3 remaining coins are good and we can use those.

If the scale didn't balance in the first place we still take 3 coins off the left side and replace them with three new coins. If the scale balances then all the coins on the scale are good and also the 3 remaining coins are good adding to 9.

If the scale still doesn't balance then we know that 1 of the 3 coins on the left are bad and we can use all the others to pay 9.
In either case we only uses the scale twice.
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