by Risk_06 on Sat Jul 01, 2006 11:33 pm
Well...if the answer isn't 3 or 5, is must be 4, right? Now how do we arrive at this solution...
From mrdexter's work, we know that the only possible combinations are:
1/4/8, 1/5/7, 2/3/8, 2/4/7, 2/5/6
How do we rule out 1/5/7, 2/3/8, and 2/5/6?
Let's go through this again...
2/3/8:
Let's skip right to Person 2, Brian. He picks up his card and finds a 3. Only choices are 1/3/9 and 2/3/8. He knows that the only possible combination is 2/3/8, since Ed (Person 3) would've known the other 2 cards, since he had a 9, and the only possible combination is 1/3/9. Since it wasn't, it has to be 2/3/8.
2/5/6:
This time, let's go to Person 3, Ed. Ed, the person on the right, picks up the card and finds a 6. Only choices are 2/5/6 and 3/4/6. It must be 2/5/6 because if it was 3/4/6, Jennifer (Person 1) would've found the 3 and known that the other 2 numbers must be 3/4/6. Since she didn't, it must be 2/5/6.
1/5/7:
Again, let's skip to the end. Brian (Person 2) looks and finds 5. It could be 1/5/7 or 2/5/6. Brian knows it must be 1/5/7 because if Ed picked up a 6, he would know that the numbers had to be 2/5/6, because Jennifer (Person 1) would've known the 2 numbers were 3/4/6. (Just like the example above).
Therefore, the answer is 4. And now I have a major migraine. >.<