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The text in the image appears to be in Georgian. Here's a translation and explanation of the problem:

**Translation:**
"On the 25th of a certain month, a certain date is 11 days earlier than the exam date, and 15 days later, it's 7 days later than the exam date. In how many months of the year can there be no exam dates and no exam months?"

**Explanation:**
The problem is about finding how many months there are in a year where a certain condition involving dates and exam dates can't occur. It provides some constraints based on a hypothetical date, such as the 25th day being a specific amount of time away from an exam date.

**Solution Approach:**
1. Let’s denote the exam date as `E` and the given date as `D = 25`.
2. We have two conditions:
   - \( D + 11 = E \)  (This implies that the exam date is 11 days after the 25th)
   - \( D + 15 = E + 7 \) (This implies the date 15 days after the 25th is 7 days after the exam date)
3. Solving the above conditions to find `E` and then checking for which months these conditions can’t hold.

Would you like a detailed solution based on this approach or further explanations? Here are some related questions that you might be interested in:

1. What is the mathematical representation of days in a month to solve this?
2. How many months have exactly 30 days?
3. What are the constraints of leap and non-leap years in date calculations?
4. How do you solve for specific dates in modular arithmetic?
5. What is the significance of constraints in mathematical problem-solving?

**Tip:** When dealing with dates and calendar problems, using modular arithmetic can simplify many problems related to wrapping around months and days.

25th of a month is 11 days before an exam, and 15 days later it is 7 days after the exam. In how many months of the year can there be no exam dates and no exam months?

Learn how to solve a date and time problem where the 25th of a month is 11 days before an exam and 15 days later it is 7 days after the exam. This problem involves modular arithmetic and date calculations, suitable for students in Grades 8-10.

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