I don't know how to logically approach this, other than to make some random assumption and continue from there until the possibility of a valid set of answers is eliminated, or until a solution is found.

Arbitrarily choosing 'A' as the answer to the first question, it then follows that 2 is
'B,' and from there, 4 is 'C.'

The answer to 3 could be 'A' or 'C,' independent of any other question.

We also know that, if this is a valid solution, there are 3 answers for 'B' altogether.
Since question 8 stipulates that only one letter correctly answers three questions, we have that 'B' must be that letter, and the answer to #8 is 'C.'

Moving on to question five, we have to count the even-numbered questions with 'B' or 'C' as their answer. Since the possible choices are 0, 1, 2, or 3, and we already have three (in 2-B, 4-C, 8-C), we know that the answer to #5 must be 'B."
Further, the answer to six cannot be 'B' or 'C;' it must be 'A' or 'D.'

Given that, the last question for which 'A' is the answer must be #6, the problem we are looking at, or #8, which we already have as 'B.' Thus, this answer must be 'A.'
The answer to the remaining question, seven, cannot be 'A.' Given the assumption we have already made in questions four and eight, there must be exactly three 'B' answers. Only two are selected thus far, and the answer to #7 is 'B.'
This makes sense, since not only are there not two consecutive Ds, there is not a single 'D' in this entire set of solutions.

Finally, number three can be either 'A' or 'C.' Since, however, question eight specifies that no letter other than 'B' is the answer to exactly three questions, and we have (so far) one 'A' and two Cs, the remaining answer must be A.

From this, the (rather, a possible) set of answers looks like:
1. A
2. B
3. A
4. C
5. B
6. A
7. B
8. C

I stopped upon finding this, due to a lack of time. I'll continue verifying or eliminating other possibilities later..

Posted by DJ on 2003-06-07 07:50:40