COVERING THE WALLS
56. A fanciful collector, who bought pictures with more regard to quantity than quality, gave instructions that the area of each frame should exactly equal that of the picture it contained, and that the frames should be of the same width all round.
At an auction he picked up a so-called “old master,” unframed, which measured 18 inches by 12 inches. What width of frame will fulfil his conditions?
A FAMILY REGISTER
57. Our family consists of my mother, a brother, a sister, and myself. Our average age is thirty-nine. My mother was twenty when I was born; my sister is two years my junior, and my brother is four years younger than she is. What are our respective ages?
58.
A spider in a dockyard unwittingly attached her web to a mechanical capstan 1 foot in diameter, at the moment when it began to revolve. To hold her ground she paid out 73 feet of thread, when the capstan stopped, and she found herself drained of silk.
To make the best of a bad job she determined to unwind her thread, walking round and round the capstan at the end of the stretched thread. When she had gone a mile in her spiral path she stopped, tired and in despair. How far was she then from the end of her task?