1) Jack wanted everything at his birthday party to go well so he prepared thoroughly. He started by placing a band of narrow red crepe paper, two feet long, on a table. Atop this band, he placed a blue one the same length. Lifting the right and left ends, he taped each together and examined what he’d done. In front of him was a blue ring, its ends taped together, sitting inside a red ring, also with its ends taped together. No, he thought to himself, that’s not sophisticated enough. He tried again, placing a piece of blue paper atop a red one as before, but this time before taping the ends together, he twisted the right ends through 180 degrees. He sat back. Now the taped ends were blue to red, and red to blue. Could he move a pencil all the way around between the inner and outer bands of paper? When Jack gently pulled the nested bands apart, how many pieces did he have?

 

2) Jack always tells the truth. He has rolled a pair of dice and says, “I didn’t roll any fours.” What are the odds that he has rolled a pair of sixes?

 

The answers to December’s puzzles were supplied in the December issue.

 

Here are the answers to this month’s puzzles:

1) Yes, he could move a pencil all the way around, separating the inner and outer bands. But when he gently separated the bands he found there was only a single long one, though it had four half-twists.