Cheryl entrusts the month to one and the day to another. When both speak, they do not describe what they know: they reveal, unintentionally, what they do not know. That's enough to find the date.
Cheryl's birthday
Riddle statement
Albert and Bernardo have just met Cheryl. She tells them that her 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
Later, Cheryl secretly tells Albert the month and Bernardo the day.
Then this conversation occurs:
- Albert: “I don't know when Cheryl's birthday is, but I know Bernardo doesn't know either.”
- Bernardo: “At first I didn't know, but now I know.”
- Albert: “Then I know it too.”
What is Cheryl's birthday?
Show solution
Solution
Answer: Cheryl's birthday is July 16.
Albert knows the month. His first sentence has two parts: he doesn't know the date, and he also knows with certainty that Bernardo doesn't either. In order to claim the latter, Albert must have received a month that does not contain any single day in the list.
In the original list, the days that appear only once are the 18th and the 19th. They appear in:
- May 19
- June 18
If Albert had received May, he could not rule out that Bernardo had the 19th and already knew the answer. The same goes for June and the 18th. Therefore, Albert did not receive May or June.
The birthday is in July or August. These dates remain:
- July 14, July 16
- August 14, August 15, August 17
Bernardo knows this reasoning and now says that he already knows the date. If I had the 14th, I couldn't choose between July 14th and August 14th. Therefore, the day is not 14.
Remaining:
- July 16
- August 15
- August 17
Finally, Albert says that now he knows it too. If your month was August, you would still have two options: the 15th and the 17th. As you already know, your month must be July.
The only July date that remains is July 16.