Computer Projects

Sample Tests

Honors Projects

Chapter 2.5 Puzzle

### This assignment is due 48 hours after the Chapter Test is given.

• Puzzle solutions are due by 5:00 PM two days after the Chapter Test.
• Puzzles are worth 5 points of extra credit each.
• Answers must be accompanied by valid reasoning. Just like the tests, the answer alone isn't enough!

"The Twin Problem"

There is a bit of trivia about the author of your textbook, Dr. James Stewart, that very few people know. He has an evil twin sister named Onad. Although he loves his sister dearly she dislikes him, and tries to be different from him in all things.

Last winter, they both went on vacation. Dr. Stewart went to Hawaii. Onad had planned on going to Aruba, but decided against it. She hates her brother so much that she was afraid there would be a chance that they might be experiencing the same temperature at the same time, and that prospect was distasteful to her. So she decided to vacation in northern Alaska.

After a few days, Dr. Stewart received a call: "this is Onad. I am very cold and uncomfortable here. That's good, since you are undoubtedly warm and comfortable, and I want us to be different. But I'm not sure why I should be the one in northern Alaska. I think we should switch places for the last half of our trip."

"It is only fair," he agreed.

So they each traveled again. Dr. Stewart took a trip from Hawaii to Alaska, while Onad took a trip from Alaska to Hawaii. They each traveled their own different routes, perhaps stopping at different places along the way. Eventually, they had reversed locations. Dr. Stewart was shivering in Alaska, Onad in Hawaii, warm and happy. She received a call from her brother.

"Hi, Onad. Guess what? At some time during our travels, we were experiencing exactly the same temperature at the same time. So HA!"

Is Dr. Stewart right? Has Good triumphed over Evil? He would try to write out a proof of his statement, but his hands are too frozen to grasp a pencil. Help him out. Either prove him right, or prove him wrong, using a mathematical argument.