How many numbers are there between 100 and 1000, which have exactly one of their digits as 7?

Explanation

To find how many numbers between 100 and 1000 have exactly one digit as 7, we can break this problem down into three cases based on the position of the digit 7 (hundreds, tens, and units).

### Step 1: Identify the range
We are looking for numbers between 100 and 1000. This means we are considering three-digit numbers where the first digit cannot be 0.

### Step 2: Case 1 - 7 in the hundreds place
If 7 is in the hundreds place, the number looks like 7XY, where X and Y are the tens and units digits respectively.
- The tens place (X) can be any digit from 0 to 9, except 7. So we have 9 choices (0, 1, 2, 3, 4, 5, 6, 8, 9).
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