# Two consecutive numbers thinking puzzle

A professor thinks of two consecutive numbers between 1 and 10.

‘A’ knows the 1st number and

‘B’ knows the second number.

**A says**: I do not know your number.

**B says**: Nor do I know your number.

**A says**: Now I know.

What are the four solutions for this?

A-3 B-4 and vice versa

A-7 B-8 and vice versa

A-2 and B-3

A-9 and B-8

Then only A able to find the number.

If A: 2 and B: 3, then A can immediately know B’s number, right? Why should he wait for ‘B’ to say that (s)he doesn’t know? Similarly, if A’s number is 9, (s)he can immediately figure that B’s is 8, right? (Both situations provided ‘between 1 and 10’ does NOT include 1 and 10. Otherwise, no solution.)

The four solutions are:

A:2, B:3 ;

A:3, B:4 ;

A:9, B:8 ;

A:8,B:7

**EXPLANATION-**

Consider the numbers between 1-10: **1,** **2,3,4,5,6,7,8,9, 10**

The fact that neither of them knows the other person’s number so they cannot have the extreme values, that are, **1 & 10.
**So we are left with 2-9.

**If the numbers known to B were 2(or 9), he could have immediately deduced the fact that the number known to A is 3(or 8). But since, he says “Nor do I know your number”, it means that number known to B is not 2, 9. HOWEVER, this does not mean that the number known to A can’t be 2 or 3.**

So, A’s number can be one of : 2, 3, 4, 5, 6, 7, 8, 9

And, B’s number can be one of : 3, 4, 5, 6, 7, 8

Now, if A’s number is 2, then he can be sure that B’s number is 3,

if A’s number is 3, then he can be sure that B’s number is 4,

if A’s number is 9, then he can be sure that B’s number is 8,

if A’s number is 8, then he can be sure that B’s number is 7.

### Your Answer

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