### Brain Teasers

# The Non-Boxer

There are three brothers: Al, Ben, and Carl. Two of the three brothers are boxers. Here are some facts:

1. The shorter of Al and Ben is the older boxer.

2. The younger of Ben and Carl is the shorter boxer.

3. The taller of Al and Carl is the younger boxer.

Which brother is not a boxer?

1. The shorter of Al and Ben is the older boxer.

2. The younger of Ben and Carl is the shorter boxer.

3. The taller of Al and Carl is the younger boxer.

Which brother is not a boxer?

### Answer

Carl is not a boxer.From fact 1, we know that Carl is not the older boxer.

From fact 3, we know that Ben is not the younger boxer.

We now have three possible scenarios:

1. Al is the younger boxer and Ben is the older boxer.

2. Ben is the older boxer and Carl is the younger boxer.

3. Al is the older boxer and Carl is the younger boxer.

If scenario 1 is true, fact 1 tells us that Ben is shorter than Al.

If scenario 2 is true, fact 1 tells us that Ben is shorter than Al; fact 3 tells us that Carl is taller than Al, making Ben shorter than Carl.

If scenario 3 is true, fact 3 tells us that Carl is taller than Al.

We can now expand our three scenarios:

1. Al is the younger, taller boxer, and Ben is the older, shorter boxer.

2. Ben is the older, shorter boxer, and Carl is the younger, taller boxer.

3. Al is the older, shorter boxer, and Carl is the younger, taller boxer.

Scenario 2 cannot be possible because it contradicts fact 2 by making the younger of Ben and Carl the taller boxer.

Fact 2 also tells us that Al is not the shorter boxer, so scenario 3 cannot be possible, either.

Therefore, scenario 1 is true, which means that Carl is not a boxer.

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