The Number Bag.
The plan is to let a person select several numbers out of a bag, and to tell him the number which shall exactly divide the sum of those he has chosen: Provide a small bag, divided into two parts, into one of which put several tickets, numbered 6, 9, 15, 36, 63, 120, 213, 309, etc.; and in the other part put as many other tickets, marked No. 3 only. Draw a handful of tickets from the first part, and, after showing them to the company, put them into the bag again, and, having opened it a second time, desire any one to take out as many tickets as he thinks proper; when he has done that, you open privately the other part of the bag, and tell him to take out of it one ticket only. You may safely pronounce that the ticket shall contain the number by which the amount of the other numbers is divisible; for, as each of these numbers can be multiplied by 3, their sum total must, evidently, be divisible by that number. An ingenious mind may easily diversify this exercise, by marking the tickets in one part of the bag, with any numbers that are divisible by 9 only, the properties of both 9 and 3 being the same; and it should never be exhibited to the same company twice without being varied.