Place 11 copies of the hexomino below in a 9x9 square such that no pair of hexominos forms a 3x4 rectangle.
| | | |
| | |
Take a square and place two equally spaced points on each side (trisecting the sides.) Starting at one corner label the points and corners around the perimeter A, B, C, D, …, L.
Connect with straight lines the pairs AI, BH, CG, DL, EK, and FJ. The resulting figure has four squares and pieces around the edge that can be rearranged to make 6 more (for a total of 10.)
How could you use a similar method to dissect a square into twenty-nine squares? How about 58? What numbers are possible by this method?