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A problem from Joseph Madachy’s Mathematics on Vacation (1966): If these statements are all true, what can we deduce about Major Perkins?

  1. Only bleary-eyed military men ever try to shave with a toothbrush.
  2. No bleary-eyed military men are at all musical.
  3. Men who never try to shave with a toothbrush never play golf.
  4. Major Perkins plays the tuba on Wednesdays.
  5. Only musical people who are golfers forget to change their socks.
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The only thing we know for certain is that Major Perkins plays the tuba on Wednesdays. All the other seeming deductions (that Major Perkins is musical, not bleary-eyed, and not a golfer; that he does not try to shave with a toothbrush, and that he remembers to change his socks) require the assumption that Perkins is a man.

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