The Cassette Recorder
You have 27 coins, each of them is 10 grams, except for 1.
The coin which is different is 9 grams or 11 grams (the coin is heavier or lighter by 1 gram).
You can use balance scales that compares what is in the two pans and compare two groups of coins to find the lighter coin.
What is the minimum number of weightings that can guarantee to find the different coin?
Ah! Click here to read the solution.
Separate the coins into 3 stacks of 9 (A, B, C).
Weigh stack A against B and then A against C.
Take the stack with the different weight (note lighter or heavier) and break it into 3 stacks of 3 (D, E, F).
Weigh stack D against E. If D and E are equal, then F is the odd stack. If D and E are not equal, the lighter or heavier (based on the A, B, C comparison) is the odd stack.
You now have three coins (G, H, I).
Weigh G and H. If G equals H, then I is the odd and is lighter or heavier (based on the A, B, C comparison).
If G and H are not equal, then the lighter or heavier (based on the A, B, C comparison) is the odd coin.
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