When is his birthday?
Richard and Jack just become friends with Harry, and they want to know when is his birthday. Harry gives them a list of ten possible dates.
| May 15 | May 16 | May 19 | |||
| June 17 | June 18 | ||||
| July 14 | July 16 | ||||
| August 14 | August 15 | August 17 |
Harry then tells Richard and Jack separately the month and the day of his birthday respectively.
Richard : I don't know when Harry's birthday is, but I know Jack doesn't know too.
Jack : At first I don't know when Harry's birthday is, but I know now.
Richard : Then I also know when Harry's birthday is.
When is Harry's birthday?
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1 solution
First we need to figure out if Richard knows the month or the day. If he knows the day, then there is no chance that Jack knows the birthday, so it must be that Richard knows the month.
From the first statement, we know that Richard is sure that Jack doesn't know the birthday, so May and June should be ruled out (the day 19 only appears in May and the day 18 only appears in June). In other words, if Richard had May or June, then he cannot be sure that Jack doesn't know, since Jack could have had 18 or 19.
Following that statement, Jack knows that May and June are ruled out.
Then, Jack is able to know which month it is. So it must be either July 16, August 15 and August 17 (not 14th as then he can't know).
Since Richard subsequently can also be sure of the date, he must know it's July. If it's August, he can't be sure as there is August 15 and 17.
So, Harry's birthday is on July 16