In our last puzzle, you were asked to determine how students embarking on their study-abroad trip to Quebec City could minimize their total distance traveled. To get to Quebec, students had to travel from Clinton, 460 miles away, on dog sleds, bringing enough food for the dogs. Sleds can only hold enough dog food to travel 300 miles at a time, but students could store as much dog food as they liked in safe caches anywhere along the route.
To minimize the distance traveled, first fill up the sled and travel 60 miles from Clinton. Cache enough food to last 180 miles. This leaves you just enough food to get back to Clinton. Repeat. You are now in Clinton, with food to last 360 miles cached 60 miles away. Fill up the sled again until you reach the first cache, at which point you fill up again, leaving enough food to travel 300 miles in the first cache, and enough food to travel 300 miles on the sled. You have now traveled 300 miles total (five trips between Clinton and the first cache), but you are still 400 miles from Quebec.
Now, build a second cache 100 miles further along the route (so 160 miles from Clinton, and 300 miles from Quebec). Drop food for 100 miles at the second cache, and go back for the remainder of the food. When you return to the second cache, you have traveled an additional 300 miles (three trips between the two caches) for a total of 600 miles. You have food on the sled to last 200 miles, and a cache of food to last 100 miles. You are now 300 miles from Quebec, so you can finish the journey, which totaled 900 miles, without further delay.
Congratulations to Evan van Tassell '13 and Linnaea Chapman '10 for winning the Third Logic Puzzle!
Have a good semester abroad! (And a Happy Thanksgiving!)