How to Take the Exam
Read all six problems. Rank them. Commit to the two you find most approachable; touch the rest only after those are WRITTEN UP.
A-1/B-1 and A-2/B-2 are designed to be solvable with the material in this course; the median competitor still scores on them by starting problem first or by leaving a correct idea unwritten. Forty minutes of clean work on an accessible problem is worth more than three hours of near-misses. If a problem asks for a value, find it numerically or by small cases FIRST, then prove it — knowing the answer transforms the search.
A complete argument with every nontrivial step justified, edge cases handled, and the conclusion stated. A correct answer with a hand-wave earns .
Name the theorems you use ("by the mean value theorem on …"). State hypotheses when you invoke them (continuity for IVT, absolute convergence for rearranging, a dominating function for swapping limit and integral). Handle the equality case of every inequality and the base case of every induction. Write in complete sentences; a solution that reads like a proof is graded like one.
Compute . Guess the pattern. Then prove it — by induction, by a bijection, by an invariant, or by an identity you now know to look for.
Most Putnam problems hide a clean answer (, , , ); small cases reveal it, and knowing the target usually reveals the method. Symmetry, extremal choices, and generating functions are the three most common "second ideas" after the pattern is found.
Re-read each written solution as a hostile grader: Is the base case there? Did you use a hypothesis you never stated? Did you divide by something that could be zero? Is the final answer boxed and consistent with your small cases? Those five minutes routinely turn a into a .