Monday, August 31, 2015

Three Puzzles Adapted from Lewis Carroll, Cont'd

1. In a certain junkyard, 60% of the cars have lost their wheels, 70% of the cars have lost their doors, and 80% of the cars have lost their seats. What is the least possible fraction of the cars that has lost all three?

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.

My answers to the puzzles are here.

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:

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