Where is the Prize?

Date: 4/17/96 at 0:2:3
From: Anonymous
Subject: Puzzle busters

After the frog turned into a handsome prince and the princess fell in 
love with him, the king said, "Not so fast! If my daughter is going to 
marry a former frog, I want to make sure he can do more than catch 
flies." And he insisted that the prince take an intelligence test. "One 
of these three boxes is filled with precious jewels. The other two 
contain pebbles from the pond you just left. As you see, the boxes all 
have inscriptions. Box No. 1 says, 'The jewelry is in this box.' Box 
No. 2 says, 'The jewelry is not in this box.' And Box No. 3 says, 'The 
jewelry is not in the first box'."

"I see," said the prince. The king continued, "If I told you how many 
of these inscriptions are true, you would be able to figure out where 
the jewelry is. Where is it?"

Date: 4/19/96 at 3:1:54
From: Doctor Joshua
Subject: Re: Puzzle busters

Hi!

I think this is really four problems, and should be divided as such:

1) Suppose all boxes are true:

Well, this can't work, because boxes 1 and 3 contradict each other.


2) Suppose only one is false:

If box 1 is false, then 2 and 3 are true, and the jewelry must be in 
box 3.

If box 2 is false, then either 1 or 3 must be false, so box 2 cannot be 
false.

If box 3 is false, then 3 really says the jewelry is in box 1. 1 and 2 
must therefore be true, so the jewelry must be in 1.


3) Suppose two are false:

Because 1 and 3 directly contradict each other, only one of the two can 
be false. If either box 1 or 3 is false, then box 2 is also false, so 
there are only two possibilities: 1 and 2 are false, or 2 and 3 are 
false.

If both 1 and 2 are false, then the jewelry would have to be in the 
second box.

Both 2 and 3 cannot be false, because this result is the jewelry is in 
both boxes 1 and 2, which cannot be.


4) Suppose all three boxes are false:

This cannot be, because then boxes 1 and 3 would contradict each other.


Ah, but the king told him that knowing how many boxes are true would 
enable him to pick the right one.  Thus, there must be one true box, 
and the correct place to look must be box 2.

-Doctors Joshua and Schwa, The Math Forum