Math Ladder · For fun, and hard
Math Competitions
Contest problems are short to state and slow to solve. They reward a fresh idea more than a long calculation. Take your time: a good problem can keep you company for days. Every solution here is written step by step, with hints first if you want a nudge instead of the whole answer.
Original challenges
Our own problems, written in the style of the Putnam, from warm-ups to very hard. Type in your answer and we check it; for a proof, read our solution and mark it done when you've proved it.
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Putnam solutions guide
The William Lowell Putnam Mathematical Competition is a contest for college students in the United States and Canada, held each year in early December: twelve problems in two sessions of three hours. Read a problem at the official link, try it, then come back for a hint or our full solution.
132 solutions ready across 11 years. The problems are © the Mathematical Association of America; we link to them and write our own solutions.