Arranging Six Squares - May 9-13, 1994 (a) How many ways can you arrange six squares in the plane so that they all share an edge with at least one other square? Two such arrangements are shown below: _ _ _ _ _ _ _ |_|_|_ _ |_|_|_|_|_| |_|_|_| |_| |_| Two configurations are considered the same if one could be derived from another by a rotation. For example, _ _ _ _ _ _ _ |_|_ _ _ _ _ |_|_|_|_|_| _ _ _ _|_| |_|_|_|_|_|_| is the same as |_|, but different from |_|_|_|_|_| (b) How many of these configurations could be folded up to form a cube? For example, _ _|_|_ _ _ _ _ _ _ _ |_|_|_|_| will work, but |_|_|_|_|_|_| will not. |_| Correct solutions to the problem were submitted by: Daniel Chan, Lenny Tang and Marlen Dias Grade 10 students at Burnaby South Secondary School, Burnaby, BC. I have also included the response from Anna Mata from Fairfield High School. While her answer is incorrect, she explained her reasoning. I suspect she has duplicate copies in there somewhere. She also talks about which hexominoes will fold up to be a cube and why. Do you think she is correct? Next problem || Previous problem || Table of Contents || Forum Home Page