Newton and Einstein just became friends with Curie, and they want to know when her birthday is. Curie gives them a list of 10 possible dates. June 16, June 17, June 20 July 18, July 19 August 15 ,August 17 September 15, September 16, September 18 Curie then tells Newton and Einstein separately the month and the day of her birthday respectively. Pay attention to their conversation. Newton: I don't know when Curie's birthday is, but I know that Einstein does not know too. Einstein: At first I don't know when Curie's birthday is, but I know now. Newton: Then I also know when Curie's birthday is. So let Curie's birthday is on x date of y month of the year. Find x + 10y

We are given a list of 10 possible dates for Curie's birthday and must determine her birthday based on the statements of Newton and Einstein. Here are the possible dates:

- June 16, June 17, June 20
- July 18, July 19
- August 15, August 17
- September 15, September 16, September 18

### Step 1: Analyzing Newton's First Statement
Newton says, "I don't know when Curie's birthday is, but I know that Einstein does not know too."

- Newton knows the month of Curie's birthday.
- If Curie's birthday were in June or July, there would be a possibility that Einstein could know the birthday, since there are unique days in these months (June 20, July 18, and July 19).
- Therefore, Newton's statement implies that Curie's birthday cannot be in June or July. This is because if the month were June or July, Einstein might be able to know the birthday based on the unique days in those months.

Thus, we eliminate all dates in June and July:
- June 16, June 17, June 20
- July 18, July 19

Remaining dates:
- August 15, August 17
- September 15, September 16, September 18

### Step 2: Analyzing Einstein's Statement
Einstein then says, "At first I don't know when Curie's birthday is, but I know now."

- Einstein knows the day of Curie's birthday.
- After Newton's statement, the remaining possible days are 15, 16, 17, and 18 in August and September.
- If the day were 15, Einstein would still be confused because there are two possible dates with the day 15 (August 15 and September 15).
- Therefore, the day cannot be 15.

We eliminate the dates with the day 15:
- August 15
- September 15

Remaining dates:
- August 17
- September 16, September 18

### Step 3: Analyzing Newton's Second Statement
Newton then says, "Then I also know when Curie's birthday is."

- Newton knows the month, and with the remaining dates being August 17, September 16, and September 18, he can now confidently determine the date.
- If the month were September, Newton would still be unsure since there are two possible dates in September (September 16 and September 18).
- Therefore, the month must be August, and the date must be August 17.

Thus, Curie's birthday is **August 17**.

### Step 4: Calculating \( x + 10y \)
- \( x = 17 \) (the day)
- \( y = 8 \) (the month, August)

We calculate \( x + 10y \):

\[
x + 10y = 17 + 10 \times 8 = 17 + 80 = 97
\]

Therefore, \( x + 10y = 97 \).

### Final Answer:
\[
x + 10y = 97
\]

Would you like further details or have any questions?

Here are 5 related questions to explore:
1. What is the significance of eliminating dates in logical puzzles?
2. How would the puzzle change if there were multiple unique days in every month?
3. What are other famous puzzles that use logic and elimination principles?
4. Could we solve this puzzle if Newton and Einstein's statements were reversed?
5. How does this puzzle demonstrate deductive reasoning?

**Tip:** When solving logic puzzles, always start by eliminating possibilities based on the given clues.

Newton and Einstein just became friends with Curie, and they want to know when her birthday is. Curie gives them a list of 10 possible dates. June 16, June 17, June 20 July 18, July 19 August 15 ,August 17 September 15, September 16, September 18. Curie then tells Newton and Einstein separately the month and the day of her birthday respectively. Pay attention to their conversation. Newton: I don't know when Curie's birthday is, but I know that Einstein does not know too. Einstein: At first I don't know when Curie's birthday is, but I know now. Newton: Then I also know when Curie's birthday is. So let Curie's birthday is on x date of y month of the year. Find x + 10y.

Discover how to solve the Curie's birthday logic puzzle using deductive reasoning. Follow the step-by-step solution based on logical elimination and the conversation between Newton and Einstein. This puzzle explores key concepts in logic puzzles and is suitable for students in Grades 9-12.

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