Answer to March 8, 1999 Problem

The Sherandomen and the Handleymen

In a certain country lived two and only two groups of people, SHERANDOMEN and HANDLEYMEN. The Sherandomen were incurable liars who never told the truth. The Handleymen were incapable of telling a lie.

A stranger, visiting in this land, asked 3 natives of the country to which groups they belonged.
The first man said something the visitor did not hear.
The second said, "He said he is a Handleyman."
The third man immediately retorted, "The first man is a liar because he is a Sherandoman."

How many Sherandomen and how many Handleymen are there among the three natives? Can you tell which ones are Handelymen and which ones are Sherandomen? Explain.



Solution:

There were two HANDLEYMEN and one SHERANDOMAN.

The first had to say, "I am a Handleyman," whether he was or not.
The second man told the truth and is a Handleyman.
If the first man lied, the third man told the truth; if the first man told the truth, the third man lied.


Correctly solved by:

No One