Five friends Andy, Brice, Cal, Danny, and Ethan make the following statements each others' ages.

Andy’s statement:
Ethan is 27.

Brice’s statement:
I am 81.

Cal’s statement:
Brice is 61.

Danny’s statements:
1. Andy is 57.
2. What Cal says is false.

Ethan’s statements:
1. Brice is older than Andy.
2. Danny is 30 years younger than Cal.

It is known that:

• None of the friends is younger than 10 or older than 99.
• Remarks made by anyone 50 or older are true, unless his age is a perfect square.
• Remarks made by anyone who is under 50 are false, unless his age is a perfect cube.

Determine the age of each of the five friends.

Brice is lying - no one would claim to be 81 (it's the equivalent of someone saying "I am a Liar" in a Knights-Liars puzzle). 

If Brice was 61, he would tell the truth, but we know he's not telling the truth.  Therefore, Cal is lying.

Since Cal is a liar, Danny is telling the truth.

Thus Andy is 57, which means he's telling the truth.

Thus Ethan is 27, which means he's telling the truth.

From Ethan's first statement we know that Brice is older than Andy.  So he's 50+ and a liar, which means his age must be either 64 or 81.  But we already know he's not 81, so he must be 64. 

From Ethan's second statement we know that Danny is 30 years younger than Cal.

Since Danny tells the truth, his age is either less than 50 and a perfect cube, or 50+ and not a square.  The only possibility for the former is 27, which would make Cal 57, but that contradicts Cal being a liar.  Thus Danny's age is 50+, and Cal's age must be a perfect square.  The only possibility is that Danny is 51 and Cal is 81. 

So we have:

Andy - 57
Brice - 64
Cal - 81
Danny - 51
Ethan - 27

Posted by tomarken on 2014-05-19 10:08:11