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.