Albertz and Bernade wanted to know Cheryl's birthday, so Cheryl gave them ten possible dates: May 15, May 16, May 19, June 17, June 18 and July/Kloc. Cheryl only told alberts her birthday and Bernade her birthday. Albertz said: I don't know Cheryl's birthday, but I know Bernade won't know either. Bernade replied: I didn't know Cheryl's birthday at first, but now I do. Alberts also replied: Then I know. When is Cheryl's birthday?

Its answer is this.

In these ten days, only 18 and 19 appeared once. If Cheryl's birthday is 18 or 19, Bernade who knows the date can guess the month and must know when Cheryl's birthday is. Why is albertz sure Bernade doesn't know Cheryl's birthday? As mentioned above, since May and June both have dates of 18 and 19, albertz who knows the month can judge whether Bernade is sure, so her birthday must be July or August. Bernade's words also provided information, because in the remaining five days in July and August, only 14 appeared twice. If Cheryl tells Bernade that her birthday is 14, then Bernade can't guess her birthday by albertz's words. So the only possible dates are July 16, August 15 and August 17. After Bernade's speech, albertz also knew Cheryl's birthday, reflecting that Cheryl's birthday month can't be in August, because there are two possible days in August and only one in July. So the answer is July 16.