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The question asks: "How many minutes are there in each day where the time on the 24-hour clock contains at least one '7'?"

To solve this, we will break it down systematically:

### Step 1: Hours containing '7'
In a 24-hour format, the hours range from 00 to 23. We need to count the number of hours that contain the digit '7':

- 07:00 to 07:59 (1 hour)
- 17:00 to 17:59 (1 hour)

Thus, there are **2 hours** (07 and 17) where the hour contains at least one '7'.

### Step 2: Minutes containing '7'
Next, we analyze the minutes for all possible hours. The minutes range from 00 to 59. We need to find how many times '7' appears in the minute's position:

- 07, 17, 27, 37, 47, 57

Thus, there are **6 minutes** in each hour where the minutes contain at least one '7'.

### Step 3: Minutes for '7' Hours
For the 2 hours that already contain '7' (07 and 17), **all 60 minutes** of those hours will count, because the '7' appears in the hour itself.

### Step 4: Minutes for Other Hours
For the remaining 22 hours (i.e., excluding 07:00-07:59 and 17:00-17:59), we only count the minutes containing '7', which we already calculated as **6 minutes per hour**.

### Total Calculation:
- In the 2 hours (07 and 17), there are **60 minutes** each.
- In the remaining 22 hours, there are **6 minutes per hour** that contain a '7'.

So the total number of minutes is:
\[
(2 \times 60) + (22 \times 6) = 120 + 132 = 252 \text{ minutes}
\]

Thus, there are **252 minutes** in each day where the time contains at least one '7'.

Would you like any further details or have any questions? Here are some related questions to explore further:

1. How would the solution change if we considered a 12-hour clock instead of a 24-hour one?
2. How many minutes contain exactly two '7's (both in the hour and minute positions)?
3. What would be the number of minutes containing the digit '5' instead of '7'?
4. How many minutes contain no '7' at all throughout a day?
5. Could this problem be generalized to find the number of minutes containing any arbitrary digit, like '3'?

**Tip**: When solving problems involving time, systematically separate hours and minutes for clarity.

How many minutes are there in each day where the time on the 24-hour clock contains at least one '7'?

Learn how to calculate how many minutes in a 24-hour clock contain the digit '7'. This problem involves basic time calculations and combinatorics, suitable for students in Grades 6-8.

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