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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.

  Submitted by K Sengupta    
Rating: 3.0000 (2 votes)
Solution: (Hide)
Inhabitant ...........Age...........Statement
A.....................38 years.........False
B............ ........39 years.........True
C.....................68 years.........False
D.....................29 years.........False
E.....................26 years.........True
F......................61 years.........True

For explanation, check out the respective solutions posted by George and hoodat in the comments section.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
SolAndre2010-05-28 18:06:42
solutionhoodat2007-02-15 13:40:16
re: PossibleK Sengupta2007-02-15 01:27:03
Some ThoughtsPossibleCharleyA.2007-02-14 22:59:53
SolutionGeorge2007-02-14 19:05:38
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