Cheryl's birthday

1. Each phrase eliminates dates because of what it implies about the knowledge of the other.
2. Start by asking yourself what months Albert couldn't have received if Bernardo could know the date from the beginning.
3. He then applies the new information to what Bernardo knows, and only at the end does he return to Albert.

Answer: Cheryl's birthday is July 16. Albert knows the month. When you say you know Bernard can't know the date either, you're ruling out months that contain single days. In the list, the only days are 18 and 19. They appear only in: - May 19;

• June 18. If Albert had received May, he could not be sure that Bernardo did not have the 19th. If he had received June, he could not be sure that Bernardo did not have 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 hears this and says that now he knows. If Bernardo had the 14th, he still wouldn't be able to decide between July 14th and August 14th. So your day is not the 14th. Remaining: - July 16;
• August 15;
• August 17. Then Albert says that now he knows it too. If your month was August, you would still have two options: August 15 and August 17. As you already know, your month must be July. The only July date left is July 16.