# Nine Puzzles of Space and Time

My friend Haym Hirsh developed these puzzles for G4G9, the ninth Gathering for [Martin] Gardner, and kindly agreed to let me blog them:

Martin Gardner’s relative Dr. Art Renaming traveled widely across the U.S. and the world. Art maintained a diary in which he described some of the puzzling circumstances he experienced over the course of his travels. What follows are excerpts from his diary. Answer the question following each diary excerpt.

1. “I am located in one of the 48 states in the Continental United States. If I go nine miles in a straight line, regardless of direction, I will leave the state I am in.” In what state was Art?

2. “I am located in one of the 48 states in the Continental U.S. If I go 90 miles in a straight line, regardless of direction, I will have needed to move my watch one hour ahead to keep it set correctly.” In what state was Art?

3. “Today is my 100th birthday. My twin brother Al is 9 minutes older than me, but his birthday won’t happen for another three days.” In what year was Art born?

4. “I’ve just gotten off the phone with my brother Al, who is in Alaska. We had a 15-minute phone call that started at 9:00am Al’s local time and ended at 9:00am my local time.” In what country was Art?

5. “Al and I are located in the same state, one of the 48 states in the Continental U.S. If I head due east, I’ll enter Canada. If Al heads due east, he’ll enter Mexico.” In what state was Art?

6. “I’ve just gotten off the phone with my brother Al. Although he had no idea where I was when the call began, and with no information beyond my solitary statement ‘It’s September 9th here’ he replied ‘I know where you are’ and correctly said what country I was in.” In what country was Art?

7. “If I proceed nine miles in a straight line, regardless of direction, I will need to set my watch 30 minutes ahead, then turn it back 30 minutes, and then finally put it ahead 30 minutes to keep it set correctly.” In what country was Art?

8. “I am in one of the great capitals of Europe. I just learned that Bob, Carl, and I are in countries that share physical borders with each other. The official language of Bob’s country is Dutch, and Carl’s is Portuguese. It is 9:00am local time for both Bob and Carl.” What was Art’s local time?

9. “I’m on a conference call with David, Edward, and Frank. We discovered that (1) although we’re all in the Continental U.S., the local time is different at each of our locations; (2) David and Edward are in the same ocean-bordering state; and (3) Frank’s local time is three hours later than mine.” In what state was Art?