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.

Suppose a problem in the queue has A responses and a score of B. Find a formula that gives the number of possible combinations 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 two possibilities: {one TU and two comments} and {two TU's and one TD}

(In reply to solution by Charlie)

Charlie, I had just finished with the same formula when I had noticed your post.  Yet, I wanted to express the formula with the variables given by Jer -- A (responses) and B (score):

[(A + |B|)/2] - |B| + 1

[ ] (square brackets) indicate the floor function

| | (pipes) indicate the absolute value function

Posted by Dej Mar on 2007-05-15 17:40:59