The Cabinet-Maker’s Problem.—A cabinet-maker had a round piece of veneering, with which he has to cover the tops of two oval stools. It so happens that the area of the stools, without the hand-holes in the centre, and the circular piece, are the same. How must he cut his veneer so as to be exactly enough for his purpose?
Circle Puzzle.—Secure a piece of cardboard, the size and shape of the diagram, and punch in it twelve holes in the position shown in the diagram. Cut the cardboard into four pieces of equal size, each piece to be of the same shape, and to contain three holes, without cutting into any of them.
Circle Puzzle.
The Nuns.—Twenty-four nuns were placed in a convent by night to count nine each way, as in the figure. Four of them went for a walk; how were the remaining nuns arranged in the square so as still to count nine each way? The four who went out returned, bringing with them four friends; how were they all arranged still to count nine each way, and thus to deceive the sister in charge, as to whether there were 20, 24, 28, or 32 in the square?
The Nuns.
Cross-Cutting.—How can you cut out of a single piece of paper, and with one cut of the scissors, a perfect cross, and all the other forms that are shown in the diagram?