Here is the vital puzzle about Cheryl’s birthday. Cheryl gives a set of days and asks her friends Albert and Bernard to guess her birthday.
May 15, May 16, May 19, June 17, June 18, July 14, July 16, Aug 14, Aug 15, Aug 17
As a clue, she gives the Month to Albert and the Date to Bernard.
Albert (has info on Month) says, “I don’t know the birthday, but I know Bernard doesn’t know either.”
Bernard (who has info on Date) says, “I didn’t know at first, but now I do.”
Albert: “Now I also know Cheryl’s birthday.”
So what is Cheryl’s birthday?
Let’s start the analysis by placing the Months and Dates in the following table.
| 14 | 15 | 16 | 17 | 18 | 19 | |
| May | X | X | X | |||
| June | X | X | ||||
| July | X | X | ||||
| Aug | X | X | X |
Looking at the table column-wise, you can find two unique numbers, 18 and 19; if Bernard (‘Date Guy’) gets those, he will quickly identify the birthday (as June 18 and May 19 are the only possibilities). But Albert (Month guy) says he knew Bernard did not know. The only way Albert can say this with confidence is because May and June were not the months he got as the clue. Let’s remove those two months from the table.
| 14 | 15 | 16 | 17 | 18 | 19 | |
| May | ||||||
| June | ||||||
| July | X | X | ||||
| Aug | X | X | X |
Now, Albert got the message. He says he knows it now. This means that the number he got was not 14; otherwise, it would have caused confusion between July 14 and August 14. Remove those as well.
| 14 | 15 | 16 | 17 | 18 | 19 | |
| May | ||||||
| June | ||||||
| July | X | |||||
| Aug | X | X |
Albert can only say he knew when it was July, the only unique Month in the table. Chery’s birthday is July 16.
Cheryl’s Birthday: Wiki
