Originally posted by wolfgang59
I give two smart guys each a piece of paper with a number on. I tell them that their numbers are consecutive integers and between 1 and N (inclusive). They can only see their own number.
Their conversation is as follows;
1st guy: "I dont know your number"
2nd guy: "I dont know your number"
1st guy: "I dont know your number"
2nd guy: "I know your number"
What was N?
1st guy: "I don't know your number"
2nd guy knows 1st guy's number is not 1 or N
2nd guy: "I don't know your number"
1st guy knows 2nd guy's number is not 1 or 2, or N or N-1
1st Guy: "I don't know your number"
2nd Guy know 1st guy's number is not 1 or 2 or 3, or N or N-2 or N-3.
2nd Guy: "I know your number"
2nd guy must have either 3 (so he knows first guys number must be 4), or 4 (so he knows first Guy's number must be 5), or N-3 (so he knows first Guys number must be N-4), or N-4 (so he knows first guys number must be N-5)
We know N must be at least 7, but it can be any number larger than that.
I think we need some other bit of information to get it such as:
"If I now told you the value of N you would know exactly what the 2nd guys number was".