Answer to May 2008 Problem of the Month

There is an island inhabited by two tribes. The natives of one tribe always tell the truth and the natives of the other tribe always lie.

On a recent trip, a visitor was confronted by three natives, but he couldn't tell which tribe they were from. See if you can tell whether they are liars or truth-tellers from the following statements:

"Oh, we're all liars," said the first native.
"Just one of us is a truth-teller," claimed the second of the three.
The third native did not speak.

How quickly can you determine each native's tribe?
(Only ONE answer will be accepted for this problem -- no second chances!).

Solution to the Problem:

The first native was a liar, the second was a truth-teller, and the third was a liar.

If the first native was telling the truth, then there is a problem with his statement, "we are all liars." So, he must be a liar. That means that his statement is false, and there must be at least one person telling the truth.

If the second native is a liar, then either there are two people telling the truth or none. But we know that they can't all be liars, and there can't be two truth-tellers since the first one is known to be a liar.
Hence, the second native is telling the truth, and that means he is the only truth-teller.
So the third native is a liar (even though he didn't speak).

Correctly solved by:

1. K. Sengupta	Calcutta, INDIA
2. John Funk	Ventura, California
3. Les Walker	Ventura, California
4. Courtney Bouton	----------
5. James Alarie	University of Michigan -- Flint Flint, Michigan
6. Clint Lamb	Mountain View High School, Mountain View, Wyoming
7. Taiya Cheney	Mountain View High School, Mountain View, Wyoming
8. Katie Woody	Mountain View High School, Mountain View, Wyoming
9. Chris Maldonado	Mountain View High School, Mountain View, Wyoming
10. Zach Williamson	Mountain View High School, Mountain View, Wyoming
11. Scott Woody	Mountain View High School, Mountain View, Wyoming
12. JoAnn Reynolds	Spring Hill, Florida
13. Jaci Egley	Mountain View High School, Mountain View, Wyoming
14. Shay Murray	Mountain View High School, Mountain View, Wyoming
15. Wynston Anglen	Mountain View High School, Mountain View, Wyoming
16. Chelsea Brunski	Mountain View High School, Mountain View, Wyoming
17. Halie Gardner	Mountain View High School, Mountain View, Wyoming