Let a "strip of squares in space" (SSS) satisfy these conditions: 1. An SSS X is a union of a collection of unit squares in R^3, with all vertices having integer coordinates. 2. Each square Q in X intersects exactly 2 other squares in the strip along *entire edges*, and these are *adjacent edges* in Q. 3. There may exist additional intersections between pairs of squares of X, as long as these are only along common vertices. Let the "size" of X be how many squares are in X. PUZZLES: ------- A. What is the smallest number of squares in an SSS that is topologically a cylinder, if possible? B. What is the smallest number of squares in an SSS that is topologically a Möbius band, if possible? (Actually I shouldn't call it a puzzle, since I don't know the answers.) —Dan