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Anyone knows how to solve the following two questions? 1. Starting with a 9×9×9 cube, Augusta removed as few 1 × 1 × 1 cubes as possible so that the resulting sculpture had front view, top view and side view all the same, as shown. How many 1 × 1 × 1 cubes did Augusta remove? 2. My grandson makes wall hangings by stitching together 16 square patches of fabric into a 4 × 4 grid. I asked him to use patches of red, blue, green and yellow, but to ensure that no patch touches another of the same colour, not even diagonally. The picture shows an attempt which fails only because two yellow patches touch diagonally. In how many different ways can my grandson choose to arrange the coloured patches correctly? G B R Y R Y G B G B Y R Y R G B |
