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
More puzzles to try-
Good to eat
I walked through a field of wheat, I picked up something good to eat, It was white and had no ...Read More »Noblest musical instrument
What is the noblest musical instrument ?Read More »Distance Traveled Puzzle
Two friends decide to get together; so they start riding bikes towards each other. They plan to meet halfway. Each ...Read More »Brown egg and white egg
If a rooster laid a brown egg and a white egg, what kind of chicks would hatch?Read More »Keys that open no locks Riddle
I have keys that open no locks, I have space, but there is no room, You can enter, but you ...Read More »25 horses 5 tracks Puzzle
Mr John have 25 horses, and he want to pick the fastest 3 horses out of those 25. He has only ...Read More »Tell The Number Of Chickens
How Many Chicken Maths Problem A farmer sold a few chickens to four different customers on a particular day. It ...Read More »The Escape Plan
As shown in the picture below, we can see a boy hanging on the tree branch to save his life. ...Read More »Akbar Birbal
To tease, King Akbar told his most clever advisor Birbal to give his daughter one thing that she can eat ...Read More »Monk on island riddle
There is an island of monks where everyone has either brown eyes or red eyes. Monks who have red eyes ...Read More »Find hidden words Resturant picture puzzle
Find 6 hidden words in this ResturantRead More »Answer if you know the color
If a white house is white and a yellow house is yellow, what color is a green house?Read More »The Bicycle
Why did the bicycle fall over?Read More »Count the Insects
An octopus has 8 legs. A hippogriff has 6 legs and 2 pairs of wings. A sphinx has 6 legs ...Read More »Which statements are true?
I am thinking of a 6-digit number. The sum of the digits is 43. And only two of the following ...Read More »Moves to fix the puzzle
We are given 100 pieces of a puzzle. If fixing two components together is counted as 1 move ( a ...Read More »colouring riddle
Consider a grid of size 4 by 4 (i.e. sixteen squares), where all squares should get a colour. The coloured ...Read More »Correct Counting
I went to city Mexico on the way I saw four women, with four bags, who have four kittens. Each ...Read More »Ants on a stick
Ants on a stick may only move left or right. If they bump into each other they bounce off of ...Read More »Height decreases with age riddle
I’m tall when I’m young and I’m short when I’m old. What am I?Read More »