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Finding "Zebedees's Number" Problem Challenging

This problem was made by: Alex Bellos This is what it said:

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? 1,2,3,4,5 or it is not possible to answer. (answer was 3)

I wasn't sure wich was the correct answer. I am also not sure what a consecutive positive integer is. Could someone please explain how this problem works. Thanks!

Note by Rocky E
3 months, 2 weeks ago

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Let the two numbers be \(x\) and \(y\), Xanthe's numbers is \(x\) and Yvette's number is \(y\). Since \(x\) and \(y\) are consecutive positive integers, \(x+1=y\) or \(y+1=x\). If \(x\) is one, then \(y\) only an be 2, since they are positive integers, but Xanthe didn't know first Yvette's number, so \(x\neq1\). If \(y=1\), then \(x=2\), and if \(y=2\), then \(x=3\), but Yvette didn't know first Xanthne's number, so \(y\neq1, 2\). Next time Xanthne knew the number, \(x=3\), because then \(y=4\) for sure, and if \(x>3\), then there are two cases, so Xanthne wouldn't know it. So \(x=3\), and \(y=4\).

Áron Bán-Szabó - 3 months, 2 weeks ago

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Thank you also Pi Han Goh for clarifying.

Rocky E - 3 months, 1 week ago

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Thank you Áron Bán-Szabó that makes way more sense now.

Rocky E - 3 months, 2 weeks ago

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I think you're referring to this question.

If "x" and "x+1" are positive integers, then they are consecutive positive integers as well.

You can look at the solution discussion to see how it's done.

Pi Han Goh - 3 months, 2 weeks ago

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