Wikipedia:Reference desk/Archives/Mathematics/2017 December 12

= December 12 =

Cheryl’s Birthday
I came across this problem (http://abc7.com/society/are-you-smart-enough-to-solve-this-riddle/656040/) and couldn’t figure it out thinking there wasn’t enough information. So I looked at the solution but I’m still not convinced. I think the problem lies with Albert’s second statement. While if you take Albert’s statement to be true you can solve it, I believe there is no way Albert could make that deduction. Am I right? —�-Polyknot (talk) 16:06, 12 December 2017 (UTC)
 * This problem is old enough that the solution is available if you just google it. Here is the first such solution I found through Google.  If you want to find others, try typing "cheryl's birthday solution" into Google.  -- Jayron 32 16:09, 12 December 2017 (UTC)
 * Thanks Jay, but there was a solution on the web page I posted. The problem I have is that, as I mentioned, I don’t see how Albert could have enough information to make his second statement. —Polyknot (talk) 16:24, 12 December 2017 (UTC)
 * Wasn't this a question in a Singapore school exam which went viral?  B was given the number 14, 15, 16, 17 or 18 (if he had been given the number 19 he would know it was May).   A must have been given May because if B had been given 19 he would know the date.   B now knows the date (it's the number given to him and the month is May).   The possible birthdays in May are the 15th and 16th (19 is out).   Originally 15 could have been May or August and 16 could have been May or July.   That's as far as I can take it. 82.13.208.70 (talk) 17:05, 12 December 2017 (UTC)
 * Albert knows (from the start) that it is July.
 * After Albert's 1st statement, Bernard and the readers know that it's either July or August.
 * Based on Bernard's statement, Albert and the readers know that the day is not 14 (if it was 14, Bernard would not know if it's July 14 or August 14).
 * So Albert knows that it is July and not 14. So he knows it is July 16. -- Meni Rosenfeld (talk) 20:37, 12 December 2017 (UTC)

We actually have an article about this. --JBL (talk) 00:47, 13 December 2017 (UTC)


 * Here are some teasers to keep you entertained over Christmas.  Answers are included, and Cheryl's birthday is explained well:

,      . 86.171.242.205 (talk) 12:16, 13 December 2017 (UTC)

Meni says the answer is 16 July and that Albert knows from the start that it's July. We can add to that that Bernard knows it's the 16th. Before anyone speaks, A knows that the date is 14 or 16, B knows that it is July or August. Albert starts off by saying

Agreed, since he knows that if B has 14 it's either July or August and if B has 16 it's either May or July. What I don't understand is why, when A speaks,

Bernard and the readers know that it's either July or August.

B certainly knows that, but how do the readers know it? Now A has spoken B says (in effect) that he knows it's July. How does he know? 86.171.242.205 (talk) 15:00, 13 December 2017 (UTC)
 * See Cheryl's Birthday. JBL linked it in "We actually have an article about this". Blue text means a link. PrimeHunter (talk) 21:04, 13 December 2017 (UTC)
 * No, before A speaks, B doesn't "know that it is July or August". He knows that it is 16, which means it is May or July.
 * After A speaks, the readers know that it is July or August, because otherwise, A could not have been sure that B doesn't know the answer. For example, let's assume it's May. So for all A knows, it could be May 19. In this case, B, knowing it's 19, would deduce that it is May, because that is the only possibility for 19. So it can't be May. It can't be June either (because then it could be June 18, in which case B would know the answer off the bat). This leaves July and August.
 * B, of course, having already known that it's May or July, can now be confident it is July. -- Meni Rosenfeld (talk) 22:14, 13 December 2017 (UTC)