Albert and Bernard have just become friends with Cheryl, and they want to know when her birthday is. Cheryl gives them a list of 10 possible dates:

May 15, May 16, May 19
June 17, June 18
July 14, July 16
August 14, August 15, August 17
Cheryl then tells Albert and Bernard separately the month and the day of her birthday respectively.

Albert: I don’t know when Cheryl’s birthday is, but I know that Bernard doesn’t know either.
Bernard: At first I didn’t know when Cheryl’s birthday was, but I know now.
Albert: Then I also know when Cheryl’s birthday is.

So when is Cheryl’s birthday?

To determine Cheryl's birthday, let's analyze the statements made by Albert and Bernard and the implications of those statements.

### List of Possible Dates
- May 15, May 16, May 19
- June 17, June 18
- July 14, July 16
- August 14, August 15, August 17

### Step-by-Step Analysis

1. **Albert's Statement:**
   - Albert knows the month but not the day.
   - Albert is certain that Bernard doesn't know either.
   
   This means the month Albert knows cannot contain a unique day that would allow Bernard to know the birthday immediately. 
   - If the month was **May** (15, 16, 19) or **June** (17, 18), Albert couldn't be certain that Bernard doesn't know the birthday because 18 and 19 are unique across all months. Thus, Albert would be uncertain if Bernard knows the birthday.
   
   Therefore, **Albert's month must be July or August**, since these months don't have unique days.

2. **Bernard's Statement:**
   - Bernard initially didn't know the birthday, but now he knows.
   - Since Bernard now knows, the day must be unique among the remaining possible dates.
   
   Remaining dates:
   - July: 14, 16
   - August: 14, 15, 17
   
   Bernard could now identify Cheryl's birthday because the day is unique among these dates. So, the possible days Bernard can identify must be 16 (from July) or 15, 17 (from August).

3. **Albert's Conclusion:**
   - Albert now knows the birthday too after Bernard's statement.
   - Since Albert also figures out the exact date, it means the month (which Albert knows) must lead to a unique day that Bernard identified.

### Final Determination
Since Albert was able to determine the exact birthday after Bernard’s realization, the month must be July.
- If the month were August, there would still be two possible dates (15 and 17).

Hence, Cheryl's birthday must be in July and the only possible date is **July 16**.

### Conclusion
Cheryl's birthday is **July 16**.

Would you like details on any part of the solution or have further questions? Here are some questions you might consider next:
1. Can you explain why May and June were eliminated in the first step?
2. What is the significance of Bernard's realization in the second step?
3. How does Albert's final realization confirm the exact date?
4. Can we verify each step to ensure there are no other possible dates?
5. How would the problem change if the list of dates were different?

**Tip:** When solving logic puzzles, carefully consider the implications of each person's knowledge and statements to narrow down the possibilities.

Explore the solution to Cheryl's birthday logic puzzle involving Albert, Bernard, and Cheryl's birthday dates. Understand the logical deductions step-by-step to determine Cheryl's birthday. Suitable for Grades 7-9.

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