CHANGING SEATS. — The following problem may be found in many of our elementary books of arithmetic: A club of eight persons agreed to dine together every day as long as they could sit down to the table differently arranged. How many dinners would be necessary to complete this arrangement? — Answer — by the well known rule of permutation, it will be found that the whole party must live 110 years and 170 days, and must eat 362,880 dinners. So rapidly does the sum roll up on this process that if the party had consisted of one more person, they would have had 443,520 dinners to get through; and if ten persons were to enter into the compact, it would be necessary for them, in order to complete their task, to live long enough to devour 3,628,800 dinners.