Alice and Bob have two positive integers, x and y respectively, glued to their foreheads, so that each can read the other's number but not their own. They also know that |x - y| = 1. The following conversation is overheard between Alice and Bob:
Alice: I don't know my number.
Bob: I don't know my number.
Alice: I don't know my number.
Bob: I don't know my number.
They say this to each other 200 times. And then we overhear them say: Alice: I know my number! Bob: I know my number too!
Can you explain the conversation and figure out the numbers x and y. You may assume that Alice and Bob each know that the other is extremely smart - so each is confident that if the other has sufficient information to deduce the answer then he/she definitely will.
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Home » Mathematics » Alice and Bob have two positive integers, x and y respectively, glued to their foreheads, so that each can read the other's number but not their own. They also know that |x - y| = 1.