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-
Right or Wrong Puzzle
Which word, if pronounced right, is wrong, but if pronounced wrong is right?Read More »Maintain 12 Count of Matchsticks
You need to remove four matchsticks from the picture below and still need to maintain the following as in the ...Read More »Crossing the Bridge Puzzle
Four people need to cross a rickety bridge at night. Unfortunately, they have only one torch and the bridge is ...Read More »Find a given number is reachable or not
There is number line ranging from -infinity to +infinity. Initially you are number 0. you can move in both directions(Moving ...Read More »Guess the name from Car’s number riddle
A boy was driving a car, a girl took a lift from her. She asked his name. Boy said – ...Read More »Number of chocolate ice creams puzzle
There is a ice cream box containing ice creams that can be either mango flavored or chocolate flavored. You know ...Read More »Who is the Doctor
A father and son were in a car accident where the father was killed. The ambulance brought the son to ...Read More »Castles in a line
A time long back, there lived a king who ruled the great kingdom of Trojan House. As a part of ...Read More »Elevator Up or Down
A woman lives in a Tall building thirty-six floors high and served by several elevators which stop at each floor ...Read More »In what year did Christmas and New Year’s fall on the same year?
In what year did Christmas and New Year’s fall on the same year?Read More »What does a man do only once in his lifetime riddle
What does a man do only once in his lifetime, but women do once a year after they are 29?Read More »Bank Account Mess-up Riddle
A guy has 10,000 in his bank on Monday. On Tuesday, they guy had 6,000 dollars in his bank, but ...Read More »Sophie’s favorite plant puzzle
Sophie who is a housemaid, She knows her boundaries well. She is good at equations. Her favorite vegetable is cauliflower. ...Read More »How many cats do you think there were?
A number of cats got together and decided to kill between them 999919 mice. Every cat killed an equal number ...Read More »Camel and Bananas Puzzle
The owner of a banana plantation has a camel. He wants to transport 3000 bananas to a market, which is ...Read More »Probable riddle
A jar contains one hundred marbles, each of which may be white or black. You pull out 100 marbles with ...Read More »What does the following represent?
What does the following represent? N N N N N N N A A A A A A A C ...Read More »How can i determine which of the guest is right ?
I organized a small get together at my home. In the party , i have a barrel with some whiskey ...Read More »Who knocked over the monitor?
Melissa and Jessica were working on the computer along with their friends Sandy and Nicole. Suddenly, I heard a crash ...Read More »Football Game
In a football game, Christina defeated Teresa by 2 – 0 but no man from either side scored. How can ...Read More »