Geometry Forum - Problem of the Week Solutions - Arranging Six Squares, May 9-13, 1994 Daniel Chan, Lenny Tang, and Marlen Dias ____________________ The following solution was given to me by Daniel Chan, Lenny Tang and Marlen Dias, grade 10 students at Burnaby South Secondary School, Burnaby, BC. We found 35 hexominoes. 11 of these made a cube. Anna Mata ____________________ There is a total of 66 patterns and 1/3 of them (22) can be folded into cubes. First, I formed all the possible patterns with six boxes in a row. I got one pattern. Then I formed 5 patterns with 5 boxes in a row. Then I formed 22 patterns with 4 boxes in a row. With 3 boxes in a row, I formed 36 patterns, and with 2 boxes in a row, I formed 2 patterns. By then, all patterns were made with one box in one row. None of the patterns with 2 boxes or more over another row of 2 boxes or more are able to be formed into cubes. And all the patterns that form into cubes have 3 rows of boxes. Of those that have 4 boxes in 1 row, only 10 of them can be formed into cubes. 10 cubes can also be formed from those with 3 boxes in 1 row. Two of the 2 patterns that have 2 boxes in one row can form into cubes. Previous page || Next problem || Previous problem || Table of Contents || Forum Home Page