Birthday problem
(apparently this is a problem given to 14/15 year olds in the Singapore school system)
Quote: www.theguardian.comRemember, Albert is told either May, June, July or August.
Bernard is told either 14, 15, 16, 17, 18 or 19
Let’s go through it line by line.
Albert: I don’t know when Cheryl’s birthday is, but I know that Bernard doesn’t know too.
All Albert knows is the month, and every month has more than one possible date, so of course he doesn’t know when her birthday is. The first part of the sentence is redundant.
The only way that Bernard could know the date with a single number, however, would be if Cheryl had told him 18 or 19, since of the ten date options only these numbers appear once, as May 19 and June 18.
For Albert to know that Bernard does not know, Albert must therefore have been told July or August, since this rules out Bernard being told 18 or 19.
Line 2) Bernard: At first I don’t know when Cheryl’s birthday is, but now I know.
Bernard has deduced that Albert has either August or July. If he knows the full date, he must have been told 15, 16 or 17, since if he had been told 14 he would be none the wiser about whether the month was August or July. Each of 15, 16 and 17 only refers to one specific month, but 14 could be either month.
Line 3) Albert: Then I also know when Cheryl’s birthday is.
Albert has therefore deduced that the possible dates are July 16, Aug 15 and Aug 17. For him to now know, he must have been told July. Since if he had been told August, he would not know which date for certain is the birthday.
The answer, therefore is July 16.
Quote: aceofspadesFound this online - seems awkwardly worded but I assume you have to determine what Cheryl's birthday is — this is above my pay grade but thought the mathletes would enjoy it
(apparently this is a problem given to 14/15 year olds in the Singapore school system)Quote: www.theguardian.comRemember, Albert is told either May, June, July or August.
Bernard is told either 14, 15, 16, 17, 18 or 19
Let’s go through it line by line.
Albert: I don’t know when Cheryl’s birthday is, but I know that Bernard doesn’t know too.
All Albert knows is the month, and every month has more than one possible date, so of course he doesn’t know when her birthday is. The first part of the sentence is redundant.
The only way that Bernard could know the date with a single number, however, would be if Cheryl had told him 18 or 19, since of the ten date options only these numbers appear once, as May 19 and June 18.
For Albert to know that Bernard does not know, Albert must therefore have been told July or August, since this rules out Bernard being told 18 or 19.
Line 2) Bernard: At first I don’t know when Cheryl’s birthday is, but now I know.
Bernard has deduced that Albert has either August or July. If he knows the full date, he must have been told 15, 16 or 17, since if he had been told 14 he would be none the wiser about whether the month was August or July. Each of 15, 16 and 17 only refers to one specific month, but 14 could be either month.
Line 3) Albert: Then I also know when Cheryl’s birthday is.
Albert has therefore deduced that the possible dates are July 16, Aug 15 and Aug 17. For him to now know, he must have been told July. Since if he had been told August, he would not know which date for certain is the birthday.
The answer, therefore is July 16.
Typical woman playing games, am I right, Ace?
I think the main reason for questions like these are to see if one is logical. All of the information and the answer are within the question, it just takes a step by step logical approach to eliminate wrong options to arrive at the correct one. You really don't need any math skills to solve this. I will admit though, this question was worded very poorly indeed. Upon first reading I thought she told her birthday to both of them, not month/date respectively.
July 16
After Albert's first statement, we can eliminate all dates in May and June. If it were May, for instance, then Bernard could have been told "19," in which case, Bernard would know the birthday is May 19. The same goes for June 18.
Once those are eliminated and Bernard states that he knows, then it can't be August 14 or July 14 because of the matching day. This leaves Aug 15, July 16, and Aug 17.
When Albert then states he also knows, then we know it can't be Aug 15 or Aug 17 because of the matching month.
The only remaining day is July 16.
Daniel, Very Elegant solution - shorter and clear than anything I've seen on Internet-land, including solutions from the Times, WSJ, Huff Post and Reuters.
I loved it because it was similar to expert play in poker and bridge, - determining/deducing the outs or odds based on "seemingly very partial information" for the actual optimal answer.
Mike's gotta flip for this.
Edit: Actually, it is more of a problem geared towards a bridge player, who deduces the hand holdings of the three other players from similar type clues during the bidding process and the standard bidding systems used. (e.g., "East" player bids 1NT, partner West responds "2c", indicating East has a strong flat hand with length in clubs and diamonds with no five-card+ in hearts or spades, and West says he has a weak hand (few face cards) but with long suits in hearts and/or spades, etc. With balancing suit distribution between east and west, then north - your partner - is less likely to have a singleton/doubleton in a suit, depending on your hand (south's) suit distriubution which is clearly visible in your hand..... Bridge bidding can get to a mathematical science.)
And....Cheryl may have asked her two male friends this question, seeking to know which of the two is the brighter one, for Darwinian purposes, hmmm....When Cheryl says "Albert! Why THANK YOU for that wonderful birthday gift, it was sooo thoughtful of you! [then goodbye, Bernie, as you're outta there...]
