17 replies to this topic

[PlayTheMindGame]

This is very, very confusing.

[jec]

What if either student lies?

[Puzzlerz]

I'd say there are 7 solutions:
2-3, 3-4, 4-5, 5-6, 6-7, 7-8, 8-9

[sloonark]

There are not seven solutions, there are only four:



The only possible numbers A could have and be certain of B's number are 2, 3, 8, and 9.

If A had any of 4, 5, 6, or 7, then he would not be certain of B's number.

[mustavarest]

Surely student B knows after student A's first statement only that A does not have have 1 or 10. Neither does he have 1 or 10 or he would have known the numbers and not responded that neither did he. At this stage either of them could still have 2 or 9 or anything between so when the first student then says he now knows the numbers it would seem that he must have 2 or 9 with the second student having 3 or 8. Unless I completely misunderstand the question this means there are only 2 possibilities when he could know the numbers at that stage - 2 and 3 or 8 and 9.

[mustavarest]

Having come across this one again, and thought about it again, I now see that after the second 'don't know' the first student clearly does not have no.1 and the second does not have 1 or 2. Equally first does not have 10 and second does not have 9 or 10. First student however then says he knows the numbers so he must have 2 or 3 or 8 or 9 with second student having 3 or 4 or 7 or 8 to make the pair. Phew!!! seems easy when the mist clears.

[Aatif]

Easy Savoury - Back to the Number Puzzles
A teacher thinks of two consecutive numbers between 1 and 10 (Edit: 1 and 10 included). The first student knows one number and the second student knows the second number. The conversation of the students is as follows:
First: I do not know your number.
Second: Neither do I know your number.
First: Now I know.
Will you find all 4 solutions?

First: 3 Second: 4
First: 2 Second: 3

First: 8 Second: 7
First: 9 Second: 8

[Llam4]

There is a lot of confusion in this thread, let me clear it up:

Since the first child does not know the other's number, he does not have a 1 or a 10. (Or he would know the other student's number would be 2 or 9 respectively.

Now the second child knows that the first child does not have a 1 or a 10, he knows that if he has a 2 or a 9 then the other child must have a 3 or an 8, respectively. He says he does not know, so therefore he does not have a 1, 2, 9 or 10.

The first child now knows that the second child does not have a 1, 2, 9 or 10, and we know that the first doesn't have 1 or 10. The only way the first child would know the answer at this point is if he has a 2, a 3, an 8 or a 9.

Explanation:
If child 1 has a 2: Child 2 does not have 1(discovered earlier) or 2(I have it), the only other consecutive number is 3.
If child 1 has a 3: Child 2 does not have a 2(discovered earlier) or a 3(I have it), the only other consecutive number is 4.
If child 1 has an 8: Child 2 does not have a 9(discovered earlier) or an 8(I have it), the only other consecutive number is 7.
If child 1 has a 9: Child 2 does not have a 10(discovered earlier) or a 9(I have it), the only other consecutive number is 8.

Therefore the only possible answers are:
2 and 3
3 and 4
7 and 8
8 and 9