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A Six Inhabitants Problem (Posted on 2007-02-14) Difficulty: 3 of 5
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.

See The Solution Submitted by K Sengupta    
Rating: 3.0000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: Possible | Comment 3 of 5 |
(In reply to Possible by CharleyA.)

If F's age is 34 then it is NOT divisible by 13. As his age is less than 40, F cannot be a Knight.
So, F is a Liar and by his statement 1, it now follows that D is a Knight, which is another contradiction.

  Posted by K Sengupta on 2007-02-15 01:27:03
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