How to systematically enumerate all possibilities of +b)+c)+d)+e? i know that when (a+b)+c=a+(b+c) then to do ((a+b)+c)+d =(a+b)+(c+d) < --"counted" all possible outer brackets =(a+(b+c))+d < -- just "slide" the brackets off =a+((b+c)+d) a+(b+(c+d)) < -- by finish '"sliding" i should get the originals questions mirror image as a result.