The Rebel Supplies Riddle: Thinking Outside the Box

You're tasked with a critical mission: ensuring the safe delivery of supplies to a rebel base deep within enemy territory. To bypass strict Imperial customs, all packages must adhere to a specific rule: if a box is marked with an even number on the bottom, it must be sealed with a red top. An urgent message arrives, revealing that one of the four boxes has been sealed incorrectly, but its identity is unknown. With the transport about to depart, which box or boxes do you need to inspect to prevent the entire shipment from being confiscated and endangering your allies?

The Logic Puzzle

The boxes are on a conveyor belt, with two facing down, displaying the numbers four and seven. The other two are facing up, one with a black top and the other with a red top. The challenge is to determine which boxes, if any, need to be checked to ensure compliance with the protocol.

Decoding the Rule

The key to solving this riddle lies in understanding the directionality of the rule. The protocol states that even-numbered boxes must have a red top. However, it doesn't say anything about odd-numbered boxes or boxes with red tops. This distinction is crucial.

Which Boxes to Inspect?

• The box marked with a seven: This box can be ignored. The rule only applies to even-numbered boxes.
• The box with a red top: This box also doesn't need inspection. The rule doesn't state that only even-numbered boxes can have red tops.
• The box with a black top: This is the box that needs to be checked. We need to ensure that it's not placed on an even-numbered box, which would violate the protocol.

The Fallacy of the Converse

The common mistake in this type of problem is assuming a symmetrical match between the number on the box and the type of lid. This error is known as "affirming the consequent" or the "fallacy of the converse." It wrongly assumes that because a condition is necessary for a result, it's also sufficient. For example, having an atmosphere is necessary for a habitable planet, but it's not the only requirement.

A Real-World Analogy

To illustrate this concept, consider a scenario involving groceries. Imagine you need to ensure that meat is not shipped to a vegetarian restaurant and that the box going to the vegetarian restaurant doesn't contain meat. In this case, it's easy to see that you only need to check the box labeled as containing meat and the box bound for the vegetarian restaurant. The other boxes don't matter.

Thinking Outside the Box

By understanding the nuances of the rule and avoiding the fallacy of the converse, you can solve the rebel supplies riddle and ensure the safe delivery of critical resources to your allies. This puzzle highlights the importance of clear thinking and attention to detail in problem-solving.

Italicized phrases are important to remember.

Bolded phrases are important to remember.