Wednesday, August 12, 2015

Three Puzzles Adapted from Lewis Carroll

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.

All three puzzles can be solved using K–12 mathematics. I have provided some hints here. Answers are here.

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