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Problem 1.
Weigh 2 against 1 and 1. If they balance, then 3 is the fake
(diagram A1). If they don’t balance and 2 is heavier then 2 is the
fake (diagram B1). If they don’t balance and 2 is light (diagram C1),
the one of the 1-buckazoid coins is fake. In this case, weigh the
1-buckazoid coins against each other. The heavier one is fake
(diagrams C2 and C3). |
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Problem 2.
Step 1. Compare the two 1-buckazoid coins. They either balance
(diagram A1) or they don’t (diagram B1). We treat each possibility
differently. If they balance, go to step 2, if they don’t balance, go
to step 3.
Step 2. We know that both 1 buckazoid coins are real, so weigh the
2-buckazoid coin against the two 1-buckazoid coins. If they don’t
balance (diagram A2), then the 2-buckazoid coin is fake. If they
balance (diagram A3), the 3-bukazoid coin is fake, and we are
finished.
Step 3. One of the 1-buckazoid coins is fake, and both the 2- and
3-buckazoid coins are real. Put the 3-buckazoid coin in one pan, and
one of the 1-buckazoid coins and the 2-buckazoid coin in the other,
and this will tell which of the 1 buckazoid coins is fake - diagrams
B2 and B3 respectively. |
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