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Step 1. Compare the two 2-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 2-buckazoid coins are real, so the fake one
is either the 1- or the 3-buckazoid coin. Weigh the 1-buckazoid and
the 3-buckazoid coin against the two 2-buckazoid coins. Obviously,
they won't balance. We now know whether the fake is too heavy (diagram
A2) or too light (diagram A3). Now put the 3-buckazoid coin in one
pan, and one of the 2-buckazoid coins and the 1-buckazoid coin in the
other. If the fake is lighter, then the lighter pan contains the fake
- this is the 3-buckazoid coin in diagram A4 and the 1-buckazoid coin
in diagram A5. If the fake is heavier, then the heavier pan contains
the fake - this is the 1-buckazoid coin in diagram A4 and the
3-buckazoid coin in diagram A5.
Step 3. One of the 2-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 2-buckazoid coins and the 1-buckazoid coin in the other,
and this will tell which of the 2-buckazoid coins is fake. If both
pans balance, then the remaining 2-buckazoid coin is the fake -
diagram B2 (from remembering the result of the weighing in diagram B1
we can say if the fake is lighter or heavier). If the pans don't
balance, the 2-buckazoid coin in the pan is the fake (diagram B3) - in
case the pan is lighter the fake is lighter, and in case the pan is
heavier the fake is heavier. |
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