Here's to obsessions. And math problems. And visual aids to thinking. And to Singapore where teaching kids how to think takes precedence over doofus regurge.
Here's the problem:
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 16 19
June 17 18
July 14 16
August 14 15 17
Cheryl then tells Albert and Bernard separately the month and the day of her birthday, respectively.
Albert: I don’t know when Cheryl’s birthday is, but I know that Bernard does not know, too.
Bernard: At first, before Albert spoke just now, I did not know when Cheryl’s birthday is. But with that added information now I do know her birthday.
Albert: Then now I also know when Cheryl’s birthday is.
When is Cheryl’s birthday?
That's a Sec 3 Singapore high school whiz-bang Olympics test question.
Hint: draw a matrix diagram. Work it through using the intensionalities/check-offs to eliminate options.
Explanation below the fold. .
Enjoy !!
So here's a combo of three explanations with adjustments and steps added to make it readable:
0. The problem is stated by the lovely Cheryl. Keep in mind that Albert gets the month; Bernard gets the day.
Apart from getting Cheryl's info, nobody knows nothing. That includes Albert, Bernard, and the problem solver/us. Then,
1. Albert states the Bernard does not know the month.
Very cute. In a flash that eliminates both May and June. Because prior to that statement, Bernard could have had the numbers 18 or 19. And in either of those cases Bernard would have known the birthday immediately.
If you've done a little 6 row by 4 column matrix, erase Col1 and Col2. What you've got left is July and August which were Col3 and Col4.
2. Bernard then states that he had not known the birthday but now with Albert's statement, he does!
Of course that eliminates 14 as the answer. A 14 could still fall in either July or August.
That leaves us with July 16th, August 15th, and August 17th as options.
3. The final step goes back to Albert using Bernard's discovery to make the final determination.
Albert solve it. But we do not, can not until Albert tells us that he has also solved it.
If Albert had been give August, then Albert would still have been left with both August 15th and August 17th as options. Bernard would have solved the puzzle; Albert would still have been in the dark.
If August, Albert would not have known the birthday.
So Albert had to have been given July for the month. He reached the same conclusion as Bernard, who got there by holding the day from Step 0 and learning to eliminate May and June from Albert.
Albert got there holding July and learning to eliminate August from Bernard.
And we get there by using their mental processes to back track to what information they had and how the added information flows inform their decisions.
Cute, eh?