Zebedee secretly writes down two consecutive positive integers. Then he tells one of the numbers to Xanthe, and the other number to Yvette (without telling them each other's number, but only telling their numbers are consecutive). The following conversation ensues:
Xanthe: "I don't know your number."
Yvette: "I don't know your number."
Xanthe: "Now I know your number!"
Yvette: "Now I know your number!"
Which of the following must be one of the two numbers?
Note: A randomly chosen correct and complete solution writer will receive a copy of Alex's new puzzle book, Can You Solve My Problems?.