Directions (25-29): Study the information carefully and answer the questions given below.

Seven friends - P, Q, R, S, T, U, and V - went to attend a cooking class for a week from Monday to Sunday, not necessarily in the same order. Each person prepared a different number of dishes during these classes.

Q prepared the most dishes. The person who prepared the least dishes attended immediately after R.S prepared the 2ndmost dishes and attended on Sunday. T and the person who prepared the second-most dishes attended on consecutive days. Q prepared 5 dishes more than T who prepared 6 dishes more than P. P attended the classes immediately after the person who prepared 9 dishes. The person who prepared 10 dishes attended immediately before the person who prepared 8 dishes. Q attended on Wednesday, while V attended on Friday. There were 2 people between R and the person who prepared 6 dishes. Only One person prepared half number of dishes than the other one.

How many persons attend class between P and the one who prepared the 2nd most dishes?

To find the number of persons who attend class between P and the one who prepared the second-most dishes (which is S), we first need to determine the schedule and the number of dishes prepared by each person based on the given information.

1. Identify the days of the week:
The classes run from Monday to Sunday:
- Monday
- Tuesday
- Wednesday
- Thursday
- Friday
- Saturday
- Sunday

2. Place the days for specific people from the clues:
- S prepared the 2nd most dishes and attended on Sunday.
- Q attended on Wednesday.
- V attended on Friday.

3. Use the clue about T and the person with the 2nd most dishes:
- S is the one who prepared the 2nd most dishes, and S attended on Sunday.
- T and the person who prepared the 2nd most dishes (S) attended on consecutive days.
- Since S is on Sunday, T must have attended on Saturday.

So far, we have:
- Monday: (Vacant)
- Tuesday: (Vacant)
- Wednesday: Q
- Thursday: (Vacant)
- Friday: V
- Saturday: T
- Sunday: S (2nd most dishes)

4. Analyze the dishes prepared by Q, T, and P:
- Let the number of dishes prepared by T be $x$.
- Q prepared 5 dishes more than T, so Q prepared $x+5$ dishes.
- T prepared 6 dishes more than P, so P prepared $x-6$ dishes.
- S prepared the 2nd most dishes, and Q prepared the most dishes.
- We are given: "There were 2 people between R and the person who prepared 6 dishes." This tells us one of the persons prepared 6 dishes.
- Another clue: "Only one person prepared half number of dishes than the other one."
- Let's analyze the possibilities for the number of dishes. If P prepared 6 dishes (since P = $x-6$):
Then T = 12 dishes, and Q = 17 dishes.
If T = 12, P = 6, Q = 17.
Let's check the half number clue: P (6) is half of T (12). This fits the condition "Only one person prepared half number of dishes than the other one".
So, P prepared 6 dishes, T prepared 12 dishes, and Q prepared 17 dishes (which is the most dishes).
Since P prepared 6 dishes, the clue "There were 2 people between R and the person who prepared 6 dishes" means there are 2 people between R and P.

5. Determine the positions of R and P:
- P attended the classes immediately after the person who prepared 9 dishes.
- Let's test the placement of R and P. The remaining days for P, R, and U are Monday, Tuesday, and Thursday.
- If P is on Thursday:
Then the person who prepared 9 dishes must be on Wednesday (Q). But Q prepared 17 dishes, which is a contradiction.
- If P is on Tuesday:
Then the person who prepared 9 dishes must be on Monday.
Since P is on Tuesday, and there are 2 people between R and P (who prepared 6 dishes), R must be on Friday. But Friday is already occupied by V. This is a contradiction.
- If P is on Monday:
P cannot attend immediately after anyone since Monday is the first day. This is a contradiction.
- If P is on Friday:
Friday is occupied by V, which is a contradiction.
- Let's re-verify the remaining slots. The days left are Monday, Tuesday, Thursday.
Wait, if P is on Thursday:
Then the person immediately before P (Wednesday) prepared 9 dishes. But Q is on Wednesday and prepared 17 dishes. This is a contradiction.
What if P is on Saturday? Saturday is occupied by T.
What if P is on Monday? No.
Let's check if P is on Tuesday, then the person on Monday prepared 9 dishes. Since there are 2 people between R and P, R can be on Friday? No, Friday is V. R can be 2 days before or after. If P is on Tuesday, 2 people between R and P means R is on Friday (since Tuesday - Wednesday - Thursday - Friday, so Wednesday and Thursday are between them). But V is on Friday, so this is not possible.
Let's try P on Monday? Not possible.
Let's try P on Thursday: 2 people between R and P means R is on Monday (Tuesday and Wednesday are between them). Let's check this:
- Monday: R
- Tuesday: (Vacant)
- Wednesday: Q (17 dishes)
- Thursday: P (6 dishes)
If P is on Thursday, the person immediately before P (Wednesday, which is Q) must have prepared 9 dishes. But Q prepared 17. Contradiction.
Wait, let's look at the schedule again:
What if P is on Friday? V is on Friday. But maybe V is not on Friday? The text says "Q attended on Wednesday, while V attended on Friday." This is fixed.
Let's check: "P attended the classes immediately after the person who prepared 9 dishes."
If P is on Saturday (T is on Saturday). Wait, S is on Sunday. "T and the person who prepared the second-most dishes (S) attended on consecutive days." This means T could be on Saturday or Monday? No, S is on Sunday, so consecutive day to Sunday is Saturday (or Monday if it wraps around, but usually Monday to Sunday is a linear week, so Saturday is the only consecutive day inside the week).
Let's try if P is on Tuesday. If P is on Tuesday, the person on Monday prepared 9 dishes. Who is on Monday? Let's say R is on Friday? No, V is on Friday. Can R be on Sunday? Sunday is S. Can R be on Wednesday? Wednesday is Q.
Wait, what if there are 2 people between R and P, and R is on Thursday? Then P is on Monday (Tuesday and Wednesday between them). If P is on Monday, there is no day before Monday.
What if P is on Friday? V is on Friday.
What if P is on Saturday? T is on Saturday.
What if P is on Sunday? S is on Sunday.
Let's check: "There were 2 people between R and the person who prepared 6 dishes."
If R is on Monday, and the person who prepared 6 dishes is P. If P is on Thursday (Tuesday and Wednesday are between Monday and Thursday). Then the person immediately before P is on Wednesday, who prepared 9 dishes. But Q is on Wednesday. Is it possible that Q did not prepare 17 dishes?
Let's re-read: "Q prepared 5 dishes more than T who prepared 6 dishes more than P."
If P prepared 3 dishes, T = 9 dishes, Q = 14 dishes.
If T = 9 dishes, then the person on Wednesday (Q) prepared 14 dishes. P is on Thursday, so the person before P (Wednesday) prepared 9 dishes. But Wednesday is Q (14 dishes).
What if P is on Tuesday? The person on Monday prepared 9 dishes. T = 12, P = 6, Q = 17. The person on Monday (who is R or U) prepared 9 dishes.
Let's test P on Tuesday. Then the person on Monday prepared 9 dishes.
We need 2 people between R and P. Since P is on Tuesday, the 2 people between them would be Wednesday and Thursday, so R must be on Friday. But V is on Friday. Wait, is it possible that R is on Tuesday and P is on Friday? No, V is on Friday.
What if P is on Thursday? 2 people between R and the person with 6 dishes (P). If R is on Monday, then R prepared 9 dishes? No, the person on Wednesday (Q) must have prepared 9 dishes for P to be immediately after them. But Q prepared 17 dishes.
What if the person who prepared 6 dishes is not P?
The text says: "Q prepared 5 dishes more than T who prepared 6 dishes more than P." This does not mean P prepared 6 dishes. It means T prepared 6 dishes *more than* P.
So, $N_Q=N_T+5$, and $N_T=N_P+6$.
If another person (say, V or R) prepared 6 dishes, then P doesn't have to be the one who prepared 6 dishes.
Let's check: "There were 2 people between R and the person who prepared 6 dishes."
If P is on Monday:
But P attended immediately after the person who prepared 9 dishes, so P cannot be on Monday.
If P is on Tuesday:
The person on Monday prepared 9 dishes.
If P is on Thursday:
The person on Wednesday (Q) prepared 9 dishes. Since Q prepared 9 dishes, then T = 4 dishes, and P = -2 dishes, which is impossible (number of dishes must be non-negative).
If P is on Friday:
But V is on Friday.
If P is on Saturday:
But T is on Saturday.
If P is on Sunday:
But S is on Sunday.
Thus, P must be on Tuesday. Since P is on Tuesday, the person on Monday prepared 9 dishes.
Since Q is on Wednesday, V is on Friday, T is on Saturday, S is on Sunday, and P is on Tuesday, the remaining people (R and U) must be on Monday and Thursday.
Since the person on Monday prepared 9 dishes, and R/U are on Monday/Thursday:
If R is on Monday:
Then Monday is R (9 dishes).
We are given: "There were 2 people between R (Monday) and the person who prepared 6 dishes."
This means the person who prepared 6 dishes must be on Thursday (since Tuesday and Wednesday are between Monday and Thursday).
So the person on Thursday (which must be U) prepared 6 dishes.
Let's check the remaining positions:
- Monday: R (9 dishes)
- Tuesday: P
- Wednesday: Q (most dishes)
- Thursday: U (6 dishes)
- Friday: V
- Saturday: T
- Sunday: S (2nd most dishes)

Let's verify the dishes:
- U prepared 6 dishes.
- Only one person prepared half the number of dishes than another. Since U prepared 6 dishes, if another prepared 12, that would be a pair (6, 12). If T prepared 12 dishes, then Q = 17 and P = 6. But only ONE person prepared half the number of dishes of another. If P = 6 and U = 6, and T = 12, then both P and U prepared half of T's dishes. So P cannot be 6.
Let's find values for T, P, Q such that no other half-relation exists, or T is not 12.
Since P is on Tuesday, and P attended immediately after the person who prepared 9 dishes (R on Monday), this is consistent.
Now we need to find the number of persons who attend class between P (Tuesday) and the one who prepared the second-most dishes (S on Sunday).
The days between Tuesday (P) and Sunday (S) are Wednesday, Thursday, Friday, and Saturday.
Thus, there are exactly 4 people (Q, U, V, T) who attend class between P and S.

Therefore, the number of persons who attend class between P and the one who prepared the 2nd most dishes is 4.