This problem involves scheduling matches for six people (A, B, C, D, E, F) across six days (Monday to Saturday) based on given constraints.

Scheduling Constraints Analysis

• Days: Monday, Tuesday, Wednesday, Thursday, Friday, Saturday.
• Constraint 1: C has a match on Friday.
• Constraint 2: Exactly three people have matches between C and F.
• Constraint 3: D has a match immediately after E, and D has a match immediately before B. This means the sequence must be E, D, B consecutively.

Step-by-Step Deduction

1. Position C: Based on Constraint 1, we place C on Friday.

   $_ _ _ _ C _$ (Mon Tue Wed Thu Fri Sat)

2. Position F: Constraint 2 states there are 3 people between C (Friday) and F. The only way to have 3 days between them within the Mon-Sat week is if F is on Monday. The days Tuesday, Wednesday, and Thursday fall between Monday and Friday.

   $F _ _ _ C _$ (Mon Tue Wed Thu Fri Sat)

3. Position E, D, B: Constraint 3 requires the sequence E, D, B. The only consecutive block of three empty days available is Tuesday, Wednesday, and Thursday.

   Therefore, E must be on Tuesday, D on Wednesday, and B on Thursday.

   $F E D B C _$ (Mon Tue Wed Thu Fri Sat)

4. Position A: The only person left is A, and the only day left is Saturday.

   $F E D B C A$ (Mon Tue Wed Thu Fri Sat)

Final Schedule and Answer

The complete schedule is:

• Monday: F
• Tuesday: E
• Wednesday: D
• Thursday: B
• Friday: C
• Saturday: A

Based on this schedule, E has the match on Tuesday.