Six inhabitants A, B, C, D, E, and F of an island are discussing their respective ages.

Each one is either a Knight (Truth teller) 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 six inhabitants.

Solution:

The ages are:
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.


Correctly solved by:

1. Kamal Lohia Holy Angel School,
Hisar, Haryana, India
2. Seth Cohen Concord, New Hampshire, USA
3. Dr. Hari Kishan D.N. College,
Meerut, Uttar Pradesh, India
4. Eloise Michael Smith Academy,
Hatfield, Massachussetts, USA