Search Puzzles

1october2010

Number Problem Solution

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?

Solution:

None of the students can have numbers 1 or 10, since they would guess the other one’s number with no problems. I will describe solutions at one end of the interval of numbers 1-10 (the same can be done on the other end).
Information that the second student does not know must be important for the first student. So the first one must expect that the second one has 1 or 3 (if the first one has 2). And as the second student does not know, then he has certainly not 1. So the first pair is 2 and 3.
If the first one had 3, then he would expect the other one to have either 2 or 4. But if the second one had 2 (and the second one would have known that the first one does not have 1), then he would know the number of the first student. However, neither the second student knows the answer – so he has 4. The second pair of numbers is 3 and 4.
Solutions at the other end of interval are 9 and 8 or 8 and 7.