Detection of birthdate

Asked Jan 15 '23 at 11:35

Active Jan 15 '23 at 18:00

Viewed 56 times

Clara’s potential birtdates,

14 July, 16 July, 15 May, 16 May, 19 May, 17 June, 18 June, 14 August, 15 August, 17 August.

Alex, Clara and Tom are friends.

Clara tells Alex month of her birthday, and tells Tom day of her birthday. Then, the following conversation occurs.

Alex: I don’t know Clara’s birthday. But, I know neither does Tom.

Tom: Originally I didn’t know Clara’s birthday. But now I know it.

Alex: I know it now too.

What is Clara’s birthdate in the possibility list?

I can’t detect it neither know how to do it.

My deductions are that

If Tom doesn’t know it at the beginning, unique days must be withdrawn.
If Alex doesn’t know it at the beginning, unique months must be withdrawn. (There is no unique month in the possibility list though)

edited Jan 15 '23 at 18:00

N. F. Taussig

76,571

asked Jan 15 '23 at 11:35

Soner from The Ottoman Empire

Please edit to include your efforts. Start by using Alex 's initial comment to define something about the birthday. – lulu Jan 15 '23 at 11:55
@lulu i did it. – Soner from The Ottoman Empire Jan 15 '23 at 11:59
Hint: The 18 and 19 appear only once. Therefore if Alex knows that Tom doesn't know then Alex knows that Clara's birthday is neither on 18th or 19th. – Alphie Jan 15 '23 at 12:04
@Alphie yeah it is what i only deduct – Soner from The Ottoman Empire Jan 15 '23 at 12:05
Well, given what Alex said, which birthdays are still possible? – lulu Jan 15 '23 at 12:10
See this – lulu Jan 15 '23 at 12:10
2

Relates: https://math.stackexchange.com/questions/1233656/albert-bernard-and-cheryl-popular-question-please-comment-on-my-theory – Henry Jan 15 '23 at 12:11
why don't you try the puzzling stackexchange: https://puzzling.stackexchange.com/ – D S Jan 15 '23 at 12:20
I would suggest that you just pick a date, and then see what each of the people can deduce, also on the basis of the other person reporting to knowing or not knowing the date. Obviously only one of the dates will lead to the outcome as presented. Don't try to think to hard about this problem at first ... just work at it and I am sure you'll eventually find the answer! – Bram28 Jan 15 '23 at 19:41

Detection of birthdate

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