Six inhabitants A, B, C, D, E, and F of an island are discussing their respective ages. Each one is either a Knight or a Liar, over 18 but under 70 years of age, and the sum of their ages is 261.

A person 40 years old or older is a knight, unless his age is a multiple of 17, and then he is a liar. A person under 40 is a liar, unless his age is a multiple of 13, and then he is a knight.

The six say:

A's Statement:
1. E is older than I am.

B's Statement:
1. A is 30 years younger than C.

C's Statement:
1. I am 51.

D's Statements:
1. C is 52.
2. I am not 29.

E's Statements:
1. A is a Liar.
2. F's age is not less than 40 years.

F's Statements:
1. D is a Liar.
2. B is 39.

Determine the ages of each of the inhabitants from the above statements.

C is a liar who is not 51, because a liar could never tell the truth about his age and 51 is a multiple of 17, so he is not a knight.

D is a liar because C cannot be 52.

F is a knight, because D is a liar.

B is a knight, because F is a knight and 39 is a multiple of 13.

C is 68, because if he were less than 40, A would be less than 10 years old, which is impossible. C is not 51, and the only other multiple of 17 <70 is 68

A is 38

A is a liar

E is a knight because he knows that A is a liar

E is younger than A, because A claims E is older.

E must be 26.


So far:

A is 38
B is 39
C is 68
D is 29
E is 26
F is a knight over 40.

26+29+38+39+68=200
261-200=61

A is 38
B is 39
C is 68
D is 29
E is 26
F is 61

Posted by George on 2007-02-14 19:05:38