Step 1: Divide the balls into three groups.
- Group 1: 3 balls
- Group 2: 3 balls
- Group 3: 2 balls
Step 2: First weighing.
- Place the 3 balls from Group 1 on one side of the scale and the 3 balls from Group 2 on the other side.
Outcome A: If the scale tips, the heavier ball is in the group on the heavier side.
Outcome B: If the scale balances, the heavier ball is in the remaining Group 3 (the 2 balls).
Step 3: Second weighing.
- If the heavier ball is in Group 1 or Group 2 (3 balls): Take any 2 balls from that group and place one on each side of the scale.
- If the scale tips, the heavier ball is the one on the heavier side.
- If the scale balances, the heavier ball is the one you didn’t place on the scale.
- If the heavier ball is in Group 3 (2 balls): Simply place one ball on each side of the scale.
The heavier ball will tip the scale.
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who needs a scale if the balls can be picked up for placement upon the scale
The solution offered is not necessarily correct. The solution is based on the assumption that 7 of the objects have exactly the same mass, which is not declared in the problem statement. Saying that one ball is slightly heavier than the others, does not necessarily mean that another ball might be lighter than the others. Therefore, the solution offered is not conclusive and will require more than 2 measurements to determine which ball has the largest mass.