# Two consecutive numbers thinking puzzle

1,406.0K Views

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?

SherlockHolmes Expert Asked on 8th March 2016 in

A-3 B-4 and vice versa
A-7 B-8 and vice versa

Krittika Curious Answered on 10th March 2016.

A-2 and B-3
A-9 and B-8

Then only A able to find the number.

vikasb Curious Answered on 10th March 2016.

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.)

on 10th March 2016.

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.

Detective Expert Answered on 11th March 2016.

• ## More puzzles to try-

• ### What is the logic behind these ?

3 + 3 = 3 5 + 4 = 4 1 + 0 = 3 2 + 3 = 4 ...Read More »
• ### Defective stack of coins puzzle

There are 10 stacks of 10 coins each. Each coin weights 10 gms. However, one stack of coins is defective ...Read More »
• ### Which clock works best?

Which clock works best? The one that loses a minute a day or the one that doesn’t work at all?Read More »
• ### (Advanced) Cheryl’s Birthday Puzzle

Paul, Sam and Dean are assigned the task of figuring out two numbers. They get the following information: Both numbers ...Read More »
• ### Five greedy pirates and gold coin distribution Puzzle

Five  puzzleFry ship’s pirates have obtained 100 gold coins and have to divide up the loot. The pirates are all ...Read More »
• ### Magical flowers!!

A  devotee goes to three temples,  temple1, temple2  and temple3  one after the other. In front of each temple, there ...Read More »
• ### Tuesday, Thursday what are other two days staring with T?

Four days are there which start with the letter ‘T‘. I can remember only two of them as “Tuesday , Thursday”. ...Read More »
• ### How could only 3 apples left

Two fathers took their sons to a fruit stall. Each man and son bought an apple, But when they returned ...Read More »
• ### How Many Eggs ?

A farmer is taking her eggs to the market in a cart, but she hits a  pothole, which knocks over ...Read More »
• ### HARD MATHS – How much faster is one train from other Puzzle

Two trains starting at same time, one from Bangalore to Mysore and other in opposite direction arrive at their destination ...Read More »
• ### Most Analytical GOOGLE INTERVIEW Question Revealed

Let it be simple and as direct as possible. Interviewer : Tell me how much time (in days) and money would ...Read More »
• ### Lateral thinking sequence Puzzle

Solve this logic sequence puzzle by the correct digit- 8080 = 6 1357 = 0 2022 = 1 1999 = ...Read More »
• ### How did he know?

A man leaves his house in the morning to go to office and kisses his wife. In the evening on ...Read More »
• ### Pizza Cost Math Brain Teaser

Jasmine, Thibault, and Noah were having a night out and decided to order a pizza for \$10. It turned out ...Read More »
• ### Which letter replaces the question mark

Which letter replaces the question markRead More »
• ### Which room is safest puzzle

A murderer is condemned to death. He has to choose between three rooms. The first is full of raging fires, ...Read More »
• ### Richie’s Number System

Richie established a very strange number system. According to her claim for different combination of 0 and 2 you will ...Read More »
• ### Srabon wanted to pass

The result of math class test came out. Fariha’s mark was an even number. Srabon got a prime!! Nabila got ...Read More »
• ### Become Normal!!

Robi is a very serious student. On the first day of this year his seriousness for study was 1 hour. ...Read More »
• ### Sakib Knows The Number!

Ragib: I got digits of a 2 digit number Sakib: Is it an odd? Ragib: Yes. Moreover, the sum of ...Read More »