A rectangular grid whose side lengths are integers greater than 1 is given. Smaller rectangles with area equal to an odd integer and length of each side equal to an integer greater than 1 are cut out one by one. Finally one single unit is left. Find the least possible area of the initial grid before the cuttings.
Just playing around on some graph paper, I eventually put the final 1x1 square in the center of an 11x11 grid. Then the remaining area cut into four 6x5 rectangles. Each of those is cut in half into a pair of 3x5 rectangles. This makes a 11x11 grid dissected into eight 3x5 rectangles and the 1x1 square, with an area of 121.
A start
