Given information:
- There are 74 students in a class.
- Each student studies at least one of the three subjects: H, E, or P.
- 10 students study all three subjects (H, E, and P).
- 20 students study H and E, but not P.
- Every student who studies P also studies H or E or both.
- The number of students studying H equals the number of students studying E.

Solution:

Step 1: Visualize the problem:
Let's create a Venn diagram to represent the given information:

```
H
/ \
/ \
/ \
/ \
/ \
/ \
/ \
/ \
/ \
/ \
/ \
/ \
E-------------------------P
```

Step 2: Fill in the given information:
- 10 students study all three subjects (H, E, and P).
- 20 students study H and E, but not P.

Step 3: Find the number of students studying each subject:
- Let's assume the number of students studying H is 'x'.
- Since the number of students studying H equals the number of students studying E, the number of students studying E is also 'x'.
- Therefore, the number of students studying P can be calculated as follows:
- Total number of students studying H, E, and P: 10 (studying all three subjects)
- Number of students studying H and E, but not P: 20
- Number of students studying P = Total number of students studying H, E, and P - Number of students studying H and E, but not P
- Number of students studying P = 10 - 20 = -10
- Since the number of students cannot be negative, this means that no student studies only the subject P.
- Therefore, all students studying P also study either H or E or both.

Step 4: Find the number of students studying H:
- Total number of students studying H: x (assuming)
- Number of students studying H and E, but not P: 20
- Number of students studying H and P: 10 (studying all three subjects)
- Number of students studying H only: x - (20 + 10) = x - 30
- Number of students studying H or E or both: x + 20 + 10 = x + 30

Step 5: Determine the value of x:
- Total number of students studying H or E or both: x + 30
- Total number of students in the class: 74
- x + 30 = 74
- x = 74 - 30 = 44

Therefore, the number of students studying H is 44.

Step 6: Check the answer:
- Total number of students studying H: 44
- Number of students studying H and E, but not P: 20
- Number of students studying H and P: 10 (studying all three subjects)
- Number of students studying H only: 44 - (20 + 10) = 44 - 30 = 14
- Number