Buckazoid Arithmetic - Basics [solution]

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Problem 1.
Weigh 2 against 1 and 1. If they balance, then 3 is the fake (diagram A1). If they donít balance and 2 is heavier then 2 is the fake (diagram B1). If they donít 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).

Problem 2.
Step 1. Compare the two 1-buckazoid coins. They either balance (diagram A1) or they donít (diagram B1). We treat each possibility differently. If they balance, go to step 2, if they donít 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 donít 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.

Posted: December 11, 2007
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