Hot and Cold
Jon Evans reports that astronomers have been discovering extrasolar planets at a fantastic rate. He says one is a planet with the catchy name PV/Nk, which has exactly four equally long seasons: winter, spring, summer, and fall. From the Coldest Day, which is in the middle of winter, to the Hottest Day, which is in the middle of summer, the temperature increases at a uniform rate. Similarly, from the Hottest Day to the Coldest Day the temperature decreases at a uniform rate. During the winter, the average temperature measured in degrees Celsius equals the average temperature measured in degrees Fahrenheit. During the summer, the average temperature measured in degrees Kelvin equals the average temperature in degrees Fahrenheit.
What is the temperature on the Hottest Day? On the Coldest Day?
The puzzle involved strange golf. On each stroke you could only hit one of two distances. On any stroke, you might fall short of the hole, drop into the hole, or drive past the hole. If the tee-to-hole distances for nine holes are 300, 250, 200, 325, 275, 350, 225, 375, and 400 yards, what two distances would you want to be able to hit?
Damon Raben showed that if you can hit 100 yards and 125 yards, you can do the course in 26 strokes. This is the best possible. Your worst scores are on the holes of length 275 and 400, which each take four shots.
However, I was not careful enough to make it clear that you were supposed to hit only in the direction of the hole, going into the hole, falling short, or driving past the hole. Several solvers pointed out that if you can hit to the side, then there are many solutions that allow you to do the course in 16 shots. Pick two different distances that match distances to holes. Then for two holes you get a hole-in-one. Each of the other seven holes can be done in two shots by shooting off to the side, and then back.
Solutions also came from William Baumann, Frank Chang, Bob Conger, Marcus Deckert, Jon Evans, Jacob Geyer, John Gutzler, John Jansen, Rob Kahn, Steve Kantor, Joe Kilroy, Stuart Klugman, John Koestner, Moshe Kofman, Casimir Ksiazek III, Chun H. Lam, Henry Ding Liu, Tim McDonald, David Oakden, Joe Pietraszewski, Sean Porreca, Yiannis Psiloyenis, Alan K. Putney, Carl A. Scheuermann, Bob Spitzer, Derek Steffan, Rob Thomas, Brad Tumbleston, and David Uhland.