Invariants, casework, and pigeonhole readiness
Use elementary olympiad-style methods such as invariant tracking, organized cases, and guarantee reasoning in visible puzzle settings.
Core · Invariants, casework, and pigeonhole readiness · Independent practice · Construction Grid
Watch: Watch whether the learner counts all calls, not just the 120 extra calls after the matched pairs are set aside. Decisive evidence is a complete response that adds the 16 matching calls and links the total to both the no-cycle bound and a 136-call construction.
Misread: A likely misread is treating callers or matched pairs as the thing to count, or treating “build one” as enough by itself. The scored answer is the total number of call edges together with a reason no larger graph works and a construction that reaches the total.
Curriculum: This task studies extremal reasoning in a balanced bipartite graph with a unique perfect matching. It scores whether the learner can use an alternating-cycle contradiction, a DAG edge bound, and a sharp construction as one coordinated proof.