Channel: singingbanana

Category: Education

Tags: birthdayjames grimeproblemmathematicsmathspuzzlemathcheryl's birthdaylogiccherylalex bellos

Description: Cheryl's Birthday problem was a question in a recent Singapore Maths Olympiad. Here is the problem: You have Albert, Bernard and Cheryl. Cheryl says "my birthday is one of these ten dates" May 15 May 16 May 19 June 17 June 18 July 14 July 16 August 14 August 15 August 17 She gives Albert the month of her birthday. And Bernard the number. Then the following conversation occurs: 1) Albert: I don’t know when the birthday is, but I know Bernard doesn’t know too. 2) Bernard: At first I don’t know when the birthday is, but now I know. 3) Albert: Then I know the birthday too. From that information, work out Cheryl's birthday. [The English is the original, slightly dodgy, English of the original question]. --- Here is Alex Bellos' post on the problem: theguardian.com/science/alexs-adventures-in-numberland/2015/apr/13/can-you-solve-the-singapore-primary-maths-question-that-went-viral And Alex solution: theguardian.com/science/alexs-adventures-in-numberland/2015/apr/13/how-to-solve-albert-bernard-and-cheryls-birthday-maths-problem And here is my reply, concentrating on that alternative answer: theguardian.com/science/alexs-adventures-in-numberland/2015/apr/15/why-the-cheryl-birthday-problem-turned-into-the-maths-version-of-thatdress --- Something from the article I wrote, which I forgot to say in the video, the alternative solution completely changes the nature of the problem, because the alternative answer can be worked out from the first two statements only. The expected answer does need all three statements. --- A bit more about that third answer. I think the reader is treating it as just a mystery date (made up of a month and number) which they have to work out. This fails to take into account that Albert has the month only, and Bernard the number only. Oh, another thing I forgot to say: the third answer is also what you get if you mix up the roles of Albert and Bernard - in which case the first statement is information about the date. --- More about the idea of "knowledge": Let p be a statement, it's either true or false. Logic is the maths of these statements. We can modify them, for example we can take not(p) which has the opposite truth value. We can add and multiply statements as well using "or" and "and". Another action is knowledge(p) which might be true or false, but is not the same as p, and the following deductions are different. So if we remove the story it becomes the difference between reading the first statement as "Bernard doesn't know" and reading it as "Albert knows Bernard doesn't know". And what you can then deduce from that. For definitions and properties of knowledge in logic, here is the wikipedia page en.wikipedia.org/wiki/Epistemic_modal_logic --- The other point I forgot to make, if this was a serious question in mathematical logic it would be written symbolically in formal logic - and there would be no ambiguity. However, this is not meant to be high level maths, it's a puzzle. So by making it accessible, and dressing it up as a puzzle, ambiguity was accidentally introduced. I sympathise with that! Writing puzzles is hard. Daniel Gjörwell in the comment made a very good point: "The intention of the author was KNOWS as REALIZE. If the first statement would have read: "I don't know but I realize that Bernard doesn't know too"; then I would have got [the correct answer]" --- If you are reading this you are in a special group of highly intelligent people who read the description in the video. Well done you. Your mission, if you choose to accept it, is to work a fish related pun into a comment without other people noticing. Good luck!