### Brain Teasers

# Tallest to Shortest

Five boys are very close in height, but they want to know how tall they are in order. If the shortest person is lying, and the rest are telling the truth, can you order how tall each boy is from tallest to shortest?

Andrew: Keith is taller than me.

Danny: I'm taller than Andrew.

Mitch: Andrew is the second tallest.

Carlos: Danny is lying.

Keith: Carlos is the third tallest.

Andrew: Keith is taller than me.

Danny: I'm taller than Andrew.

Mitch: Andrew is the second tallest.

Carlos: Danny is lying.

Keith: Carlos is the third tallest.

### Answer

Keith, Andrew, Carlos, Mitch, DannyThe way we can determine this is by looking at Andrew's statement. If he's lying, he's the shortest, and Keith is shorter than him. This is impossible because no one can be shorter than the shortest. Andrew and Keith must be telling the truth. That means Carlos is the third tallest, so he isn't lying. That means Danny is lying and is the shortest. Mitch must be telling the truth, so Andrew is the second tallest. Since Keith is taller than Andrew, he must be the tallest and Mitch must be the second shortest.

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