Andy: > Hi Diane! Am I right in thinking you're the one who has at our booth > calculating that there are 96 ways you can arrange your pieces in > Treehouse? Wooop wooop Geek Alert wooop wooop Huh, I get 204. I think one issue is that orientation of the entire row matters. 1<, 2<, 3< is distinct from 3>, 2>, 1>, even though they have a large pointing at the medium, which points at the small. Specifically... There are four "classes" of arrangements: A. Three separate pyramids. There are 6 possible orders for the pyramids: 1 2 3, 1 3 2, 2 1 3, 2 3 1, 3 1 2, 3 2 1 For each pyramids there are three directions it could point: <, ^, > That makes 6*3*3*3 = 162 arrangements. B. A stack of two pyramids to the left of a single pyramid. There are 6 possible orders for the pyramids: 1/2 3, 1/3 2, 2/1 3, 2/3 1, 3/1 2, 3/2 1 The stack is always upright, but there are three possible orientations for the lone 'mid. That makes 6*3 = 18 arrangements. C. A single pyramid to the left of a stack of two. As with class B, there are 18 arrangements. D. All three pyramids in a stack. There are 6: 1/2/3 (a tree), 1/3/2, 2/1/3, 2/3/1, 3/1/2, 3/2/1 (a nest) 162 + 18 + 18 + 6 = 204 Ryan