Inspired by Alex Bellos

Logic Level 3

Zebedee secretly writes down two consecutive positive integers between 1 and 10 inclusive. 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!"

How many possibilities are there for the ordered pair \((\)Xanthe's number, Yvette's number\()?\)



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