Explanation
Solving
To find the minimum number of weightings for n items where one is different, we use the base-3 logic because a balance scale has three possible outcomes (Left heavy, Right heavy, or Balanced). The formula is 3k≥n, where k is the number of weightings.
Step 1: First Weighting
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Divide the 8 balls into three groups: Group A (3 balls), Group B (3 balls), and Group C (2 balls).
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Weigh Group A against Group B.
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Outcome 1: If A = B, the heavy ball is in Group C (2 balls).
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Outcome 2: If A > B, the heavy ball is in Group A (3 balls).
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Outcome 3: If B > A, the heavy ball is in Group B (3 balls).
Step 2: Second Weighting
Conclusion:
In all scenarios, the heavy ball is identified in exactly 2 weightings.
31=3 (can identify 1 ball out of 3)
32=9 (can identify 1 ball out of 9)
Since 8≤9, only 2 weightings are required.
