November 2010
Problem of the Month

True or False?
by Robert Stanton in GAMES

Here is another logic puzzle that takes place on that same mythical island where every native is either a Truthteller who never lies or a Liar who never tells the truth.

A tourist encountered four natives and asked, "How many of you four guys tell the truth?"

The first one smiled and said, "More than one."

The second one said, "At least two."

The third said, "Fewer than four."

The fourth one said, "Exactly three."

The tourist smiled and said, "Sounds like three to me.   That was easy."

Was he right?   How many of the four -- if any -- were Truthtellers, and which ones were they?

Solution to the Problem:

The answers are:
The tourist was wrong.   There is only one Truthteller, and it is the third man.

If we assume all four are truthful, then the fourth statement is false, so that contradicts the assumption.

If we assume that only three are truthful, then all four statements are true, so that contradicts the assumption.

If we assume that only two are truthful, then the first three statements are true, so that contradicts the assumption.

So, either zero or one is truthful.   In either case, the statement "Fewer than four" is true, so the third man is the one Truthteller.

Correctly solved by:

1. Austin Hale	Mountain View High School, Mountain View, Wyoming
2. John C. Funk	Ventura, California
3. Levi Harmon	Mountain View High School, Mountain View, Wyoming
4. Jacob Harmon	Mountain View High School, Mountain View, Wyoming

Send any comments or questions to: David Pleacher