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        riddles >> medium >> Do you know your number now?
        
(Message started by: Noke Lieu on Feb 29^th, 2012, 4:29pm)

Title: Do you know your number now?
Post by Noke Lieu on Feb 29^th, 2012, 4:29pm

Alice and Bob each have one of two consecutive positive integers written on their foreheads.

Alice sees Bob’s number, and Bob sees Alice’s number.

Taking turns to ask "Do you know your own number?" is there is a way for them to find out the number on their own forehead?

Title: Re: Do you know your number now?
Post by towr on Feb 29^th, 2012, 10:27pm

Yes, as long as they're perfect logicians and answer the question when they can.

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turn 1, if Alice doesn't know it eliminates 2-1
turn 2, if Bob doesn't know it eliminates 1-2 and 2-3
turn 3, if Alice doesn't know it eliminates 3-2 and 4-3
turn 4, if Bob doesn't know it eliminates 3-4 and 4-5
etc
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