June 2024
Problem of the Month
Knights and Liars
Submitted by K. Sengupta, Calcutta, India
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.