When a problem is being voted on in the Perplexus queue, the journeymen and scholars post comments and vote on the problem. A "thumbs up" (TU) scores +1 point, a "thumbs down" (TD) scores -1, and a comment with no vote scores 0.
Part one of this problem, which deals with combinations of TU and TD votes can be found here.
Suppose a problem in the queue has A responses and a score of B. Find a formula that gives the number of possible permutations of TU's, TD's and nonvoting comments the problem has received.
Note: For example a problem with 3 responses and a score of +1 has six possibilities:
(In reply to solution
It's apparent from the table that N(A,B) = N(A-1,B-1) + N(A-1,B) + N(A-1,B+1). I don't know if that will be helpful in finding a closed formula that doesn't use Sigma notation.
Posted by Charlie
on 2007-05-23 15:46:24