A puzzling logic problem for middle school “mathletes” in Singapore has gone viral online. Not only could I not solve the puzzle but after reading the question it seemed to me the info given couldn't possibly provide enough to go on for anyone, no matter how bright, to come up with the answer. Here's the problem, with an explanation of the answer also given below. I *think* I understand the solution now I have had the assistance provided but I recognize that anyone who could work this out (middle school pupils no less) without it being explained is so far above my feeble intellectual abilities I can only pay my humble respects. See if you have better *luck*. Can you figure out when Cheryl’s birthday is?
Here’s the question: Albert and Bernard just became friends with Cheryl, and they want to know when her birthday is. Cheryl gives them a list of 10 possible dates. May 15 May 16 May 19 June 17 June 18 July 14 July 16 August 14 August 15 August 17 Cheryl then tells Albert and Bernard separately the month and the day of her birthday respectively. Albert: I do not know when Cheryl’s birthday is, but I know that Bernard does not know too. Bernard: At first I don’t know when Cheryl’s birthday is, but I know now. Albert: Then I also know when Cheryl’s birthday is. So when is Cheryl’s birthday? Give up? Here's the answer and an explanation: Albert is given the correct month, and Bernard is given the correct day. Possible dates: May: 15, 16, 19 June: 17, 18 July: 14, 16 August: 14, 15, 17 Albert speaks first: “…I know that Bernard does not know too” Why would he say this? If Cheryl told Bernard 18 or 19, then Bernard would know with certainty Cheryl’s birthday (there is only one 18 date and only one 19 date, 18th June and 19th May) How could Albert know with certainty that Cheryl did not tell Bernard 18 or 19? Cheryl must have told Albert a month other than May or June! Possible dates: July: 14, 16 August: 14, 15, 17 Bernard: “…I know now” Bernard must have deduced from Albert’s statement that Cheryl must have told Albert the month July or August. How does this help Bernard deduce Cheryl’s birthday? If Cheryl told Bernard the 14th is her birthday, this does not help. There is the 14th July and the 14th August. It would be impossible to know which date is correct, but if Cheryl told Bernard 15, 16 or 17, then Bernard would know with certainty Cheryl’s birthday. This is because there is only the 16th July, 15th August and 17th August left. Possible dates: July: 16 August: 15, 17 Bernard knows the answer but we do not! Albert: “Then I also know when Cheryl’s birthday is” How? Albert must have reasoned that Cheryl told Bernard 15, 16 or 17. If Cheryl told Albert the month was August, then the possible dates would be 15th August and the 17th August. If Cheryl told Albert the month was August, it is impossible for Albert to know Cheryl’s birthday. What if Cheryl told Albert the month was July? The only answer would be the 16th July! Cheryl must have told Albert the month was July. This is the only way Albert can know with certainty Cheryl’s birthday.
