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Hi Jack
I will give you a detailed answer to question 2. This also answers
question 1, but question 1 can be done in a number of ways. Can you do
it starting with 5 coins on each side? 6 on each side?
First weighing
Weigh 4 against 4, leaving the remaining 4 aside. Mark the coins on the
left
red, those on the right blue and the coins left aside green.
The first weighing balances.
In this case we know that the odd coin is green.
Second weighing
Weigh one red and one green against two green.
- If they balance then the odd coin is the one green that has not
been weighed.
Third weighing
Weigh the unweighed green against any other to see if it is light
or heavy.
- If, on the second weighing, the left side is heavy then
either the green coin on the left is too heavy or one of the
green coins on the right is too light.
Third weighing
Weigh the two green coins that were in the right pan on the
second weighing. If they balance then the green coin in the
left pan on the second balance is the odd coin and it is
heavy. If they don't balance then the lighter of the two
is the odd coin.
- If, on the second weighing, the left side
is light then either the green coin on the
left is too light or one of the green coins
on the right is too heavy.
Third weighing
Weigh the two green coins that were in the
right pan on the second weighing. If they
balance then the green coin in the left pan
on the second balance is the odd coin and
it is light. If they don't balance then the
heavier of the two is the odd coin.
The first weighing does not balance.
In this case we know that the odd coin is not green.
Second weighing
Weigh one red and three green against three red and one blue.
- If they balance then one of the three blues not weighed on the second
weighing is the odd coin, and you can tell by the first weighing whether
it is too light or too heavy.
Third weighing
Weigh two of these blue coins. If they balance the third is the odd
one and if they don't balance you know which is the odd coin.
- If the left side is heavy then either the red coin on the
left is heavy or the blue coin on the right is light.
Third weighing
Weigh the red coin on the left side in the second weighing
against any other red coin. If they balance then the blue
coin on the right in the second weighing is the odd coin
and it is light. If the two reds don't balance then the heavier
is the odd coin.
- If the right side is heavy then either the
red coin on the left is light or the blue coin
on the right is heavy.
Third weighing
Weigh the red coin on the left side in the
second weighing against any other red coin.
If they balance then the blue coin on the
right in the second weighing is the odd coin
and it is heavy. If the two reds don't balance
then the lighter is the odd coin.
Cheers
Harley |
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