Introduction / Context:
This classroom pairing puzzle applies a constraint on consecutive pairings. Once two students have studied together seven periods in a row, they cannot be paired again immediately. Additional preferences also apply (Carter refuses to work with Adam).
Given Data / Assumptions:
- Adam and Baxter have reached the maximum 7-period streak and cannot be paired this period.
- Carter and Dennis have a 3-period streak but have no rule preventing a change.
- Carter does not want to work with Adam.
- We must choose Baxter’s partner among available classmates.
Concept / Approach:
Exclude prohibited pairs first. Baxter cannot be with Adam due to the seven-in-a-row cap. Carter refuses Adam, but that does not affect Carter pairing with Baxter. Dennis can partner with Baxter, but we should also preserve flexibility and avoid creating new conflicts if unnecessary.
Step-by-Step Solution:
Remove Adam as a partner for Baxter (violates the 7-in-a-row rule).Consider Carter: allowed, and does not violate any preference (Carter’s objection is to Adam).Consider Dennis: also allowed; however, there is no stated need to maintain Carter–Dennis specifically.Any valid partner distinct from Adam is acceptable; Carter is a straightforward compliant choice.
Verification / Alternative check:
Pairing Carter with Baxter respects all constraints: the seven-in-a-row cap and Carter’s refusal (which applies only to Adam).
Why Other Options Are Wrong:
Adam: explicitly prohibited by the seven-in-a-row rule.Dennis: feasible, but the question seeks the best assignment under given notes; Carter is directly indicated as acceptable and resolves his refusal without conflict.Forest: presumably the teacher; not a student partner.“No one” contradicts the implied requirement to form pairs.
Common Pitfalls:
Misreading Carter’s refusal as a restriction on Carter’s general pairing rather than only with Adam.
Final Answer:
Carter
Discussion & Comments