A local television station sent out questionnaires to determine if viewers would rather see a

documentary, an interview show, or reruns of a game show. There were 700 responses with the
following results:
210 were interested in an interview show and a documentary, but not reruns.
28 were interested in an interview show and reruns but not a documentary.
98 were interested in reruns but not an interview show.
168 were interested in an interview show but not a documentary.
70 were interested in a documentary and reruns.
42 were interested in an interview show and reruns.
56 were interested in none of the three.
How many are interested in exactly one kind of show? its hard help..

To determine the number of people interested in exactly one type of show, we need to analyze the given information step by step.

Let's start by labeling the three types of shows:
- A = Documentary
- B = Interview show
- C = Reruns of a game show

We are given the following information:
- The total number of responses is 700.
- 210 were interested in both B (interview show) and A (documentary), but not C (reruns).
- 28 were interested in both B (interview show) and C (reruns), but not A (documentary).
- 98 were interested in C (reruns), but not B (interview show).
- 168 were interested in B (interview show), but not A (documentary).
- 70 were interested in both A (documentary) and C (reruns).
- 42 were interested in both B (interview show) and C (reruns).
- 56 were interested in none of the three.

We can construct a Venn diagram to visualize the information:

```
A (Documentary)
/
_________
| |
B | | C
(Interview)| | (Reruns)
Show | |
|_________|
\
None
```

Now, let's fill in the values we know based on the given information:

- The number of respondents interested in A (Documentary) only can be calculated by subtracting the overlaps from the total number of respondents interested in A. From the diagram, we can determine that this is 210 (A) - 70 (A∩C) = 140.
- Similarly, the number of respondents interested in B (Interview Show) only is 168 (B) - 210 (B∩A) - 42 (B∩C) = -84. Since this value is negative, it means that there is no one interested in B only.
- The number of respondents interested in C (Reruns) only can be determined in the same way: 98 (C) - 70 (A∩C) - 42 (B∩C) = -14. Again, a negative value means no one is interested in C only.
- The number of respondents interested in None of the three types can be directly obtained from the given information, which is 56.

Now, to find the number of respondents interested in exactly one type of show, we sum up the values obtained for each type:

Number of respondents interested in exactly one show = A only + B only + C only

Number of respondents interested in exactly one show = 140 + (-84) + (-14)

Number of respondents interested in exactly one show = 140 - 84 - 14 = 42

Therefore, there are 42 respondents interested in exactly one kind of show.