create a 5 week tennis schedule where 5 men play tennis doubles each week with each man at rest equally at every player plays with each man against every combination of men

To create a 5-week tennis doubles schedule where 5 men (let's call them A, B, C, D, and E) play tennis doubles, and each man is at rest equally while also ensuring that every man plays both with and against every other man, we need to carefully arrange the matches. The conditions you mentioned require a balance of rest times, partnerships, and opponents across 5 weeks.

Here’s a possible schedule that satisfies the constraints:

### Week 1:
- **Match 1**: A & B vs C & D  
- **Rest**: E

### Week 2:
- **Match 1**: A & C vs B & E  
- **Rest**: D

### Week 3:
- **Match 1**: A & D vs C & E  
- **Rest**: B

### Week 4:
- **Match 1**: B & D vs A & E  
- **Rest**: C

### Week 5:
- **Match 1**: B & C vs D & E  
- **Rest**: A

### Analysis:
- Each player rests **exactly once** (A rests in Week 5, B in Week 3, C in Week 4, D in Week 2, and E in Week 1).
- Each player plays **with every other player** at least once across the five weeks.
- Each player plays **against every other player** as well, ensuring variety in pairings and competition.

This setup meets the conditions of rest balance, partnering, and opponent variation across the five weeks.

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Do you want further details on how the scheduling ensures balanced pairings or have any other questions?

Here are 5 related questions that expand on this:

1. How would the schedule change if we wanted to rotate court positions as well?
2. What if we introduced a 6th player? How could the matches and rest periods be balanced?
3. How can this type of schedule be adapted for a singles tournament instead of doubles?
4. How can we track the individual scores or points for each player across the weeks?
5. What would be the best way to modify this schedule if a player is unavailable for one week?

**Tip:** When designing balanced schedules, it's often helpful to use combinatorial techniques to ensure fairness and diversity across matches.

Discover how to create a 5-week tennis doubles schedule for 5 players where each man rests equally and plays with and against every other player. This problem involves combinatorial scheduling principles, ideal for students in Grades 10-12.

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