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Sagot :
Answer:
Explanation:
To identify the one ball with an unknown weight (either heavier or lighter) among 12 balls in three steps using a balance scale, you can use the following method:
### Step-by-Step Method:
1. **First Weighing:**
- Divide the 12 balls into three groups of 4 balls each.
- Weigh two groups against each other (4 balls vs. 4 balls).
**Scenario A:** If the scales balance, then the irregular ball is in the group not weighed (remaining 4 balls).
**Scenario B:** If the scales do not balance, then the irregular ball is in one of the groups on the scale, and you know which group is heavier or lighter.
2. **Second Weighing:**
- Take the group of 4 balls that contains the irregular ball (from the unbalanced or remaining group).
- Divide these 4 balls into two groups of 2 balls each.
- Weigh the two groups (2 balls vs. 2 balls).
**Scenario A:** If the scales balance, the irregular ball is one of the two remaining balls not weighed.
**Scenario B:** If the scales do not balance, then the irregular ball is in the group on the scale that is heavier or lighter.
3. **Third Weighing:**
- Take the 2 balls that contain the irregular ball (from the unbalanced or remaining group).
- Weigh these 2 balls against each other (1 ball vs. 1 ball).
**Scenario A:** If the scales balance, the irregular ball is the one not weighed.
**Scenario B:** If the scales do not balance, the irregular ball is the one that is heavier or lighter.
### Summary:
- **First Weighing:** 4 balls vs. 4 balls
- If balanced, the irregular ball is in the remaining 4 balls.
- If unbalanced, the irregular ball is in the unbalanced group.
- **Second Weighing:** 2 balls vs. 2 balls (from the identified group of 4 balls)
- If balanced, the irregular ball is in the remaining 2 balls.
- If unbalanced, the irregular ball is in the unbalanced group.
- **Third Weighing:** 1 ball vs. 1 ball (from the identified group of 2 balls)
- If balanced, the irregular ball is the one not weighed.
- If unbalanced, the irregular ball is the one that is heavier or lighter.
By following this method, you can identify the ball with an unknown weight among the 12 balls in just three weighings.
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