Question:
If \( g = 3 \), what is the minimum possible number of times for which the weighing machine is to be used?
If \( g = 3 \), what is the minimum possible number of times for which the weighing machine is to be used?
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When sample size is too small, use binary decision tree logic to determine minimum steps required.
Updated On: Jul 28, 2025
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The Correct Option is C
Solution and Explanation
Only 3 coins per box means we cannot use the standard encoding technique with many coin samples.
We can treat the problem as a search over 10 possibilities. If we use binary weighing logic, each weighing gives log\(_2\) of choices. To distinguish among 10 boxes: \[ 2^n \geq 10 \Rightarrow n \geq 4 \] So minimum 4 weighings are needed to identify the heavier box.
We can treat the problem as a search over 10 possibilities. If we use binary weighing logic, each weighing gives log\(_2\) of choices. To distinguish among 10 boxes: \[ 2^n \geq 10 \Rightarrow n \geq 4 \] So minimum 4 weighings are needed to identify the heavier box.
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