Inquiries-Week 8: Fence Maxing

IntroductionPentominoes are shapes made from 5 squares joined edge-to-edge. There are 12 of them:Next, let's define what an enclosed area is with these shapes. The pentominoes must create a fence where they touch edge-to-edge with no overlaps. Note that corners touching is not closed because it is not edge to edge: ActivityBuild a fence with all 12 pentominoes, edge-to-edge, no overlaps. If you have manipulatives, Polypad or toys that can make them you can use those, or use the tool below (full page version). Now that you've made an area here are some challenges:Maximize the amount of areaMaximize the number of separate areas you can getMake the area inside a rectangleMake the shape on the outside a rectangleMake the shape on the inside and outside a rectangleA quick note: These challenges have a rich history. Pentomino fences have been explored in Martin Gardner's 1960s columns, and by Solomon Golomb, Sivy Farhi, Michael Keller, Rodolfo Kurchan, and many others. Any variation I add…