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:
{+1,0,0}
{0,+1,0}
{0,0,+1}
{+1,+1,-1}
{+1,-1,+1}
{-1,+1,+1}

(In reply to re: solution -- recurrences by Charlie)

These are apparently the Trinomial Coefficients.

Also, this link, gives a closed form involving "a regularized hypergeometric function".

Edited on May 23, 2007, 4:05 pm

Posted by Charlie on 2007-05-23 16:00:10