Book Exercise Lanes

Complete P1–P20 first, then select extra exercises for a diagnosed weakness. Use the reading guide to locate the topic in MCS or Rosen.

Lane	Select	Evidence
Counting	One labeled/unlabeled comparison and one inclusion-exclusion problem	Counted set, fiber sizes, overlap contribution
Recurrences	One structural recurrence and one coefficient problem	Bases, disjoint cases, corrected series equation
Graph models	One invariant obstruction and one explicit isomorphism	Full vertex bijection or invariant proof
Trees/routes	One tree equivalence and one Euler/Hamilton comparison	Theorem hypotheses and a checked path/trail witness
Coloring/matching	One coloring lower bound and one deficient-neighborhood case	Feasible witness and impossibility/optimality certificate
Planarity	One embedding and one forbidden-subdivision problem	Face incidence accounting and obstruction mapping

Record book, edition, section, problem ID, first attempt and assistance. Solve a different unaided problem after feedback. Do not count rereading a worked example as independent performance or require fabricated mistakes to fill a quota.