Step-by-step Solution:

Quick Solution & Analysis

Your thinking is correct. Based on a strict logical deduction of the rules, the answer can be determined. The answer key stating "Cannot be determined" is flawed.

The puzzle asks us to find B's partner for the next game. The best way to solve this is to list all possible ways the four players can be paired and then use the rules to eliminate the invalid options.

1. List All Possible Pairings

With four players (A, B, C, D), there are only three distinct ways to form two pairs:

1. Pairing 1: (A, B) and (C, D)
2. Pairing 2: (A, C) and (B, D)
3. Pairing 3: (A, D) and (B, C)

2. Eliminate Invalid Pairings

Now, let's check these three possibilities against the rules for the next game:

• Rule: "A and B have played seven games in a row" and "no pair can play together more than seven times in a row".
  This means the pair (A, B) has reached its limit and is not allowed.
  This eliminates Pairing 1.
• Rule: "C does not to work with A."This means the pair (A, C) is not allowed.
  This eliminates Pairing 2.

3. Conclusion

- After eliminating the invalid options, only one possible pairing remains for the next game: Pairing 3, which is (A, D) and (B, C).
- Since this is the only possible arrangement, the pairings are uniquely and logically determined.
- The question asks, "Who should play with B?". In this single valid scenario, B's partner must be C.

Final Answer: The person who should play with B is C.