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 the cooking class between P and the one who prepared the second-most dishes, we can analyze the clues step-by-step to reconstruct the schedule and the number of dishes prepared by each friend.

1. Days of the Week:
The week runs from Monday to Sunday:
- Monday
- Tuesday
- Wednesday
- Thursday
- Friday
- Saturday
- Sunday

2. Placing the Friends on Days:
- S prepared the 2nd most dishes and attended on Sunday. (S = Sunday, 2nd most dishes)
- Q attended on Wednesday. (Q = Wednesday)
- V attended on Friday. (V = Friday)

3. Using the Clue about T and S:
- T and S (the person who prepared the 2nd most dishes) attended on consecutive days.
- Since S is on Sunday, T must be on Saturday. (T = Saturday)

4. Calculating the Number of Dishes:
- Let the number of dishes prepared be represented by their names.
- Q prepared the most dishes.
- S prepared the 2nd most dishes.
- Q prepared 5 dishes more than T, who prepared 6 dishes more than P.
$Q=T+5$
$T=P+6$
- This implies:
$Q=P+11$
- Since S prepared the 2nd most dishes and Q prepared the most, the ranking of dishes from highest to lowest starts as: Q > S > T > P ...
- We are given: "The person who prepared the 10 dishes attended immediately before the person who prepared 8 dishes."
- "P attended the classes immediately after the person who prepared 9 dishes."
- "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."

5. Determining P's position and the Days:
- Since T is on Saturday, Q is on Wednesday, V is on Friday, and S is on Sunday, the remaining days for P, R, and U are Monday, Tuesday, and Thursday.
- "P attended the classes immediately after the person who prepared 9 dishes."
- If P is on Monday, the person before P would be on Sunday (which is S, who prepared the 2nd most dishes). Let's see if S prepared 9 dishes. If S = 9, then Q must be greater than 9. Since Q > S > T > P, we have Q > 9 > T > P.
- If T prepared 6 dishes more than P, and Q prepared 5 dishes more than T:
If S = 9, and S is 2nd most, then Q is the most, so Q > 9. Since T is less than S, T ≤ 8.
If T = 8, then P = T - 6 = 2. Then Q = T + 5 = 13. This fits the order Q(13) > S(9) > T(8) > P(2).
Let's check the clue: "P attended the classes immediately after the person who prepared 9 dishes." Since S (who prepared 9 dishes) attended on Sunday, and the week wraps around or Monday is immediately after Sunday: P would attend on Monday.
If P is on Monday:
- Monday: P (2 dishes)
- Tuesday: (The person who prepared the least dishes attended immediately after R. So if R is on Monday, Tuesday has the least dishes. But P is on Monday. If R is on Tuesday, then Thursday has the least? No, Wednesday is Q. Let's check.)
Let's place the remaining people: R and U. The available days are Tuesday and Thursday.
If R is on Tuesday, then the person who prepared the least dishes attended immediately after R, which would be Wednesday (Q). But Q prepared the most dishes, which is a contradiction. Therefore, R cannot be on Tuesday.
Thus, R must be on Thursday. The person immediately after R is V (on Friday), so V prepared the least dishes.
If R is on Thursday, then U must be on Tuesday.
So the schedule is:
- Monday: P (2 dishes)
- Tuesday: U (6 dishes - let's check the clue: "There were 2 people between R and the person who prepared 6 dishes." The people between R (Thursday) and the person with 6 dishes are Wednesday and Tuesday, or Friday and Saturday. If Tuesday is the person with 6 dishes (U), then there are 2 days (Wednesday, Tuesday? No, between Thursday and Tuesday is only 1 day: Wednesday. Between Thursday and Monday: 2 days (Tuesday, Wednesday). So P (Monday) has 6 dishes? But we calculated P = 2. Let's re-evaluate).
Let's look at the days between R (Thursday) and the person with 6 dishes: if the person with 6 dishes is Monday (P), then the days between Monday and Thursday are Tuesday and Wednesday (2 people: U and Q). This matches perfectly! Thus, P prepared 6 dishes.
If P = 6 dishes:
- T = P + 6 = 12 dishes.
- Q = T + 5 = 17 dishes.
Since S prepared the 2nd most dishes, and Q (17) is the most, S must have prepared more than T (12). So S has 13, 14, 15, or 16 dishes.
- "P (Monday) attended the classes immediately after the person who prepared 9 dishes." The day before Monday is Sunday (S). So S prepared 9 dishes. But S must be the 2nd most, and 9 is less than T (12), which contradicts S > T. Let's re-verify.
The day before P is Sunday (S). If S prepared 9 dishes, then S is 9. But Q = 17, T = 12. S cannot be the 2nd most if T is 12 and S is 9. Therefore, P cannot be on Monday.
Let's try P on Thursday:
The person before P is Wednesday (Q). So Q prepared 9 dishes. But Q is the most, and if Q = 9, then T = 4, P = -2, which is impossible.
Let's try P on Tuesday:
The person before P is Monday. So the person on Monday prepared 9 dishes.
If P is on Tuesday:
We have Q (Wednesday), V (Friday), T (Saturday), S (Sunday), P (Tuesday).
The remaining days are Monday and Thursday. The remaining friends are R and U.
- "There were 2 people between R and the person who prepared 6 dishes."
If R is on Monday, the days between Monday and Thursday are 2 (Tuesday, Wednesday). So the person on Thursday must have prepared 6 dishes.
If R is on Thursday, the days between Thursday and Monday are 2 (Tuesday, Wednesday). So the person on Monday must have prepared 6 dishes. But we know the person on Monday prepared 9 dishes. Thus, R must be on Monday, and the person on Thursday (which is U) prepared 6 dishes (U = 6).
Let's check: "The person who prepared the least dishes attended immediately after R." Since R is on Monday, the person immediately after R is Tuesday (P). So P prepared the least dishes.
Since U = 6, and P prepared the least, P < 6.
Let's check the dishes relations:
- T = P + 6
- Q = T + 5 = P + 11
Since P is the least, and U = 6, P must be less than 6.
Let's look at: "Only One person prepared half number of dishes than the other one."
Also: "The person who prepared 10 dishes attended immediately before the person who prepared 8 dishes."
The consecutive days with 10 and 8 dishes must be:
- Monday (R) and Tuesday (P): R=10, P=8. But P is the least (less than U=6), so this is impossible.
- Tuesday (P) and Wednesday (Q): P=10, Q=8. Impossible as P is the least and Q is the most.
- Wednesday (Q) and Thursday (U): Q=10, U=8. But U is 6. Impossible.
- Thursday (U) and Friday (V): U=10 (but U=6, impossible).
- Friday (V) and Saturday (T): V=10, T=8. If T=8, then P = T-6 = 2. Since P=2, T=8, Q = T+5 = 13. This works! Let's check: V=10, T=8. But the clue says: "The person who prepared 10 dishes attended immediately before the person who prepared 8 dishes." So Friday (V) is 10, Saturday (T) is 8. This matches!
Let's check the values:
- P (Tuesday) = 2 dishes
- T (Saturday) = 8 dishes
- Q (Wednesday) = 13 dishes
- R (Monday) = 9 dishes (since P on Tuesday attended immediately after the person who prepared 9 dishes, which is Monday (R))
- U (Thursday) = 6 dishes
- V (Friday) = 10 dishes
- S (Sunday) = 2nd most dishes. Since Q=13 is the most, and the other known values are R=9, P=2, U=6, V=10, T=8, S must be 11 or 12. Let's check the half relationship: "Only One person prepared half number of dishes than the other one."
Let's list the numbers of dishes: 9, 2, 13, 6, 10, 8, S.
Pairs with one being half of another:
- If P=2 and U=6 (not half)
- If P=2 and T=8 (not half)
- If U=6 and Q=13 (not half)
- If V=10 and S = 5? S must be 11 or 12. If S=12, then U(6) and S(12) is a half pair. Also T(8) and P(2) (not half). If S=12, the only half pair is U(6) and S(12). This fits the condition perfectly!

Let's summarize the days and people:
- Monday: R (9 dishes)
- Tuesday: P (2 dishes)
- Wednesday: Q (13 dishes)
- Thursday: U (6 dishes)
- Friday: V (10 dishes)
- Saturday: T (8 dishes)
- Sunday: S (12 dishes, which is the 2nd most)

6. Answering the Question:
We need to find how many persons attend class between P (Tuesday) and the one who prepared the 2nd most dishes (S, Sunday).
The days between Tuesday and Sunday are:
1. Wednesday (Q)
2. Thursday (U)
3. Friday (V)
4. Saturday (T)

Thus, there are 4 persons (Q, U, V, T) who attend class between P and the one who prepared the 2nd most dishes.