2. A bag contains one counter, known to be either white or black. A white counter is put in, the bag shaken, and a counter drawn out, which proves to be white. What is now the chance of drawing a white counter?
3. Consider that:
- 3 divides evenly into 9.
- 37 divides evenly into 999.
- 7 divides evenly into 999999.
Show that any odd number not divisible by 5 divides evenly into 99...9, if you include enough 9's.
You can find the original versions of these puzzles in Carroll's book Pillow Problems—a beautiful edition of which I discovered recently in a used bookstore in Berkeley, California. Here is the eye-catching cover design: