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)

My independent computations are in conformity with Charlie's result.

Let us denote:

c = the value of the score

d = # responses

f = the number of possible combinations of TU's, TD's and

nonvoting comments the problem has received.

After some algebraic manipulations we arrive as the same result in terms of the previous post, which is:

f = [0.5*(abs(c) + d)] – abs(c) + 1;

where abs(x) = absolute value of x and:

[x]= the greatest integer< = x.

*Edited on ***May 18, 2007, 6:29 am**