93. How many phone numbers contain the combination 12? (The number consists of six digits.)
93. Let's consider the following five sets of phone numbers:

![](https://cdn.mathpix.com/cropped/2024_05_21_683be32ee1eca857285bg-117.jpg?height=159&width=242&top_left_y=319&top_left_x=255)

![](https://cdn.mathpix.com/cropped/2024_05_21_683be32ee1eca857285bg-117.jpg?height=107&width=240&top_left_y=544&top_left_x=256)

B

![](https://cdn.mathpix.com/cropped/2024_05_21_683be32ee1eca857285bg-117.jpg?height=107&width=243&top_left_y=368&top_left_x=510)
-

![](https://cdn.mathpix.com/cropped/2024_05_21_683be32ee1eca857285bg-117.jpg?height=152&width=229&top_left_y=315&top_left_x=750)

E

![](https://cdn.mathpix.com/cropped/2024_05_21_683be32ee1eca857285bg-117.jpg?height=109&width=244&top_left_y=541&top_left_x=737)

(for example, set \( B \) consists of numbers where the second and third digits are 12, and the other digits can be anything). Each of these sets contains \( 10^4 \) numbers. Sets \( A \) and \( B \) do not have any common numbers. Sets \( A \) and \( C \) have \( 10^2 \) common numbers, which are numbers of the form

![](https://cdn.mathpix.com/cropped/2024_05_21_683be32ee1eca857285bg-117.jpg?height=111&width=246&top_left_y=997&top_left_x=505)

It is easy to calculate that there are \( 6 \cdot 10^2 \) numbers that belong to any two sets simultaneously. Finally, only one number (1212 12) belongs to three sets. Now, using either the method from problem 91 or the method from problem 92, it is easy to show that the desired number is \( 5 \cdot 10^4 - 6 \cdot 10^2 + 1 = 49401 \).

## Chapter 3