Daily Math Puzzle: 2026-09-02
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2026-09-02
In the 'Automaton Prime' factory, three robot types – Worker, Guard, and Scout – are produced. Each robot uses one unique core processor: Workers use Processor A, Guards use Processor B, and Scouts use Processor C. Recently, a quality control audit revealed that exactly ONE of these processor types (A, B, or C) was manufactured incorrectly. All robots equipped with this faulty processor type will malfunction, while robots with correct processors function perfectly. During the audit, the following observations were made on a batch of 100 robots: - All 30 Worker robots are functioning perfectly. - Exactly half of the 40 Guard robots are malfunctioning. - All 30 Scout robots are malfunctioning. Based on these observations, which processor type is the faulty one?
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Solution
Processor C — Let's analyze the observations based on the rule that *all* robots equipped with the faulty processor type will malfunction, and robots with correct processors function perfectly, and exactly one processor type is faulty:
1. **Worker robots (Processor A):** All 30 Worker robots are functioning perfectly. This immediately tells us that Processor A cannot be the faulty one. If Processor A were faulty, all 30 Worker robots would be malfunctioning.
2. **Guard robots (Processor B):** Exactly half of the 40 Guard robots are malfunctioning. This is the tricky part. The puzzle states that *all* robots equipped with the faulty processor type *will* malfunction. If Processor B were the faulty type, then *all* 40 Guard robots (which use Processor B) would be malfunctioning, not just half of them. Therefore, Processor B cannot be the faulty one.
3. **Scout robots (Processor C):** All 30 Scout robots are malfunctioning. This observation perfectly aligns with the condition for a faulty processor type. If Processor C is the faulty one, then all robots using it (the Scouts) should malfunction, which they do.
Since we've determined that Processor A and Processor B are not faulty, and the puzzle states that exactly *one* processor type is faulty, it logically follows that **Processor C** must be the faulty one. The information about the Guard robots serves as a distractor, requiring careful application of the 'all robots will malfunction' rule.
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