Step-by-step Solution:

Quick Solution and Analysis

Important Note: This is a classic logic puzzle. The correct answer is 2 weighings. The answer key provided in the image (C. 3) is incorrect for this specific problem where you have 8 balls and know that one is heavier. The explanation below shows why 2 is the correct answer.

Method 1: Step-by-Step Weighing

The strategy is to divide the balls into three groups for each weighing. A balance scale has three possible outcomes (left down, right down, or balanced), allowing us to eliminate two-thirds of the possibilities with each step.

Weighing 1:

• Divide the 8 balls into three groups: Group A (3 balls), Group B (3 balls), and Group C (2 balls set aside).
• Place Group A on the left pan and Group B on the right pan of the balance.
• Outcome A: If the pans balance, the heavy ball is not among the 6 balls you weighed. It must be in the leftover Group C (which has 2 balls).
• Outcome B: If one side goes down (e.g., the left side), the heavy ball must be in that group (Group A, which has 3 balls).

After just one weighing, we have already narrowed down the search to a smaller group of either 2 or 3 balls.

Weighing 2:

• If the heavy ball is in the group of 2 (from Outcome A):Place one of these two balls on each pan. The side that goes down holds the heavier ball. The process is finished.
• If the heavy ball is in the group of 3 (from Outcome B):Take any two of the three suspect balls and place one on each pan, leaving the third ball aside.
  
  • If the pans balance, the heavy ball must be the one you set aside.
  • If one side goes down, that ball is the heavy one.

In all possible scenarios, the heavier ball is guaranteed to be identified in a maximum of 2 weighings.

Method 2: Mathematical Formula

The minimum number of weighings (n) required to find one odd ball from a group of (B) balls using a balance scale is the smallest integer 'n' that satisfies the formula:

3ⁿ ≥ B

• In this case, the number of balls (B) is 8.
• For n = 1, 3¹ = 3 (which is less than 8).
• For n = 2, 3² = 9 (which is greater than or equal to 8).

The smallest integer 'n' that satisfies the condition is 2.

Logically Correct Answer: The minimum number of weighings required is 2.