A Dime a Dozen
2025-09-22
Part 1
You bought 12 special dimes at a yard sale. After getting them inspected by your local numismatist, he determines one is a counterfeit due to it being slightly heavier than the others.
Once you get home, you find out that you've mixed up the coins. All you have to determine which coin is counterfeit is a balance scale.
What is the least number of weighs you can use to determine which coin is counterfeit?
Part 2
Suppose you don't know whether the counterfeit coin is heavier or lighter than the other coins.
How can you determine which coin is counterfeit and whether it's heavier or lighter than the real coins using only 3 weighs?
Solution
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