mr x

[23birdman23]

Have you seen this? I can't do it, not sure if there is a piece missing?? Can you help?!

Dr X's birthday is Nth of M. Dr X wanted his students, A and B, to guess his birthday

A knows the month M.
B knows the day N.

Both of them were told that Dr X's birthday is one of ten dates below:

4th march
5th march
8th march
4th june
7th june
1st september
5th september
1st december
2nd december
8th december

Dr X asked if they had figured out his birthday?

A said: "if I don't know the answer, then there's no way B would know the answer"
B then said: "actually I didn't know before, but now I know Dr X's birthday".
A finally said: "Oh, in that case, I know too".

[barmy]

I would suggest 7th June as tis date is the only one containing a unique day and unique month.

No scientific reason though...

[gen2]

Firstly barmy It cannot be June 7th (nor Dec 2nd) because B would have known immediately what the birthday was.

The answer to the puzzle is Sept 1st

The answer to 23birdman23 is No, there is not a piece missing. There is sufficient information stated to deduce from the answers given by A & B that the date is Sept 1st.

[QueenComp]

Please xplain how you worked that out I woul dlove to understand it, i couldn't do it for love nor money!

[squarebear]

"B" knows it is the 1st. So from that he knows that the month that "A" knows is either September or December.

"A" says he doesn't know, so "B" thinks, "well if it was December, "A" would think it was the 2nd, as that only appears in December's days. And as "A" doesn't know, it must be September".

I think...

[gen2]

Sorry everyone. I have just tried to put my thought processes into words to explain, and you know what? Suddenly it doesn't look as convincing. Maybe I'm wrong after all?. I'll come back to this later this afternoon and try to convice myself what is correct.

[MatydaLover]

If I understand the question correctly ...

They both eliminate 2nd December and 7th June otherwise B would know the answer immediately.

June is now a unique month, but since A still doesn't know the answer it can not be 4th June. Hence A's statement.

But B now knows the answer. The only way that B can have the answer, is if it is 4th March - 4 being the only unique day. Hence B's statement.

A can see this and thus now knows the answer as well. Hence A's second statement.

[gen2]

Yes, I have now come to the same conclusion

March 4

sorry for any confusion caused earlier.