Hardest Math Exam: IMO, Putnam & STEP Compared
If you love math puzzles and wonder which contest will push you to the limit, you’re in the right place. The International Mathematical Olympiad (IMO), the Putnam Competition, and the UK’s STEP (Sixth Term Examination Papers) are often called the hardest math exams. Each tests a different skill set, but all share sky‑high difficulty and a reputation for separating the truly elite.
What Makes a Math Exam “Hard”?
Hardness isn’t just about tricky numbers. It’s a mix of time pressure, abstract thinking, and unfamiliar concepts. The IMO expects you to solve proof‑based problems that can take hours of deep reasoning. The Putnam adds a college‑level twist, demanding clever shortcuts and creative insight. STEP sits between them, focusing on rigorous problem solving for university admissions, with questions that often need an elegant, concise solution.
IMO – The Global Benchmark
IMO is a two‑day, six‑question marathon. Each problem scores up to 7 points, and you only get 4.5 hours per day. The toughest part? You must write full proofs, not just give a numeric answer. Topics range from number theory to geometry, and the problems are designed to be unsolvable with standard school tricks. Success comes from years of practice, studying past papers, and learning proof techniques like induction, invariants, and extremal arguments.
Practical tip: start a “problem of the day” routine. Solve one IMO problem every morning, write a clean proof, and compare your solution with official solutions. Over time you’ll spot recurring patterns and build a toolbox of methods.
Putnam – College‑Level Brain Teaser
The Putnam is a six‑hour, 12‑question test held twice a year in the U.S. and Canada. Each question is worth 10 points, but most top scorers only solve 5–7 problems. The questions are notorious for hidden tricks; a problem may look simple, but the path to the answer demands a surprising insight.
To crack Putnam, practice with “solution sketches.” When you see a problem, first write a quick outline of possible approaches before diving into calculations. This habit saves time and helps you avoid dead‑ends. Also, study classic Putnam problems—they often reuse elegant ideas like generating functions or clever counting arguments.
STEP – The UK University Gatekeeper
STEP consists of three 2‑hour papers, each with six questions. Universities like Cambridge use it to test analytical thinking beyond school exams. The hardest STEP questions look like advanced high‑school problems, but they demand precise reasoning and neat presentations.
Best preparation strategy: work on past STEP papers under timed conditions. After each paper, rewrite your solutions on a clean sheet, focusing on clarity. Teachers and online forums can point out common pitfalls such as unjustified steps or missing cases.
Overall, the “hardest” label depends on your background. If you’re a high‑schooler, IMO might feel brutal. If you’re in college, Putnam could be the tougher hurdle. For UK students aiming for top universities, STEP is the gate you must clear. Whichever exam you target, the key is consistent practice, learning proof techniques, and reviewing official solutions. Start small, track your progress, and you’ll see the hardest problems become manageable challenges.