# A teacher thinks of two consecutive numbers between 1 and 10. The first student knows one number..............

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A teacher thinks of two consecutive numbers between 1 and 10. The first student knows one number and the second student knows the second number. The following exchange takes place:
First: I do not know your number.
Second: Neither do I know your number.
First: Now I know.
What are the 4 solutions of this easy number puzzle?

posted Oct 14, 2014

2-3
3-4
7-8
9-10

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

The fact that neither of them knows the other person's number so they cannot have the extreme values, that are, 2 & 9.

So we are left with 3-8.

Case 1:

If A can immediately guess the number when B doesn't have the solution that means A has a 3 or a 8 and B a 4 or a 7 respectively.
OR
A=8, B=7

Case 2: Similarly A and B can interchange positions
Therefore,
A=4, B=3
OR
A=7, B=8

So these are the four cases.

Similar Puzzles

This is definitely one of the harder number puzzles on this site.
A teacher says: I'm thinking of two natural numbers greater than 1. Try to guess what they are.
The first student knows their product and the other one knows their sum.
First: I do not know the sum.
Second: I knew that. The sum is less than 14.
First: I knew that. However, now I know the numbers.
Second: And so do I.
What were the numbers?

+1 vote

Using the digits 1, 2, 3 and 4, find the number of 10-digit sequences that can be written so that the difference between any two consecutive digits is 1.

Examples of such 10-digit sequences are 1234321232 and 2121212121.

Difference between squares of two numbers is 8. Twice the square of first number by square of second number is 19. What are the numbers?