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.

A:  Liar  -   38
B:  Knight - 39
C:  Liar  -   68
D:  Liar  -   29
E:  Knight - 26
F:  Knight - 61

C must be a liar since he could not truthfully claim to be 51.  D must be a liar since he assigned the age of a Knight to Liar C.  This makes D 29 years of age.  F is a Knight since he correctly named D as a Liar.  This makes B 39 years of age and a Knight.  Since A is 30 years younger than Liar C, C cannot be under 57 years of age.  Therefore, C must be 68 (multiple of 17).  This makes A 38 years old and a Liar.  We now know that E is less than 38.  Since E correctly stated that A is a liar, he must be a Knight of age 26.  The second clue by E is overdefined since we now can subtract the sum of the five known ages from 261 to get 61 for F.

Posted by hoodat on 2007-02-15 13:40:16