Mathcastle
From Grade 4 to the Putnam — learn from twenty book-style courses, practice 141,000+ problems with step-by-step solutions, sit sixty real-format contests, climb a 3D castle, duel your friends, and keep a streak. All in one place, all free.
Or explore without an account — take the placement quiz to find your level.
Have a great problem in mind? Anyone can suggest problems for MathCastle — the best ones become daily challenges.
Suggest a problemFrom warm-ups to olympiad stumpers — typed answers, instant checking, and a step-by-step worked solution behind every single problem.
Twenty book-style courses: Grade 4 through Calculus, then Multivariable Calculus, Linear Algebra, and Differential Equations, and the whole competition ladder — AMC 8/10/12, AIME, USAMO, and a 19-topic Putnam course. Every formula proved, worked problems on every page, printable booklets.
Feynman’s trick, King and Queen rules, Glasser’s master theorem, Frullani, Beta and Gamma, the reflection formula, Wallis, Fresnel — taught with full proofs and a verified problem pool of their own.
141,000+ problems at five difficulty levels with step-by-step solutions. A placement quiz finds your level, the ladder climbs and drops with you, and course practice saves your place.
Numbered practice sets for AMC 8/10/12, MathCounts Sprint & Target (real four-pair Target timing), AIME, and two-sitting USAMO and Putnam tests — every set unique to its contest and to the games, with official scoring, an answer sheet, arrow-key navigation, and a printable PDF with full solutions.
A 3D castle and a 3D tower you climb floor by floor, the Countdown race, Problem Rush with a green review rail — hand-crafted Arena problems, plus a fresh Daily, Weekly, and Event challenge.
Missed problems come back on a spaced-repetition schedule you can arrow through, every problem you solve lands in your Archive, and a mastery dashboard tracks each technique.
Paper that typesets LaTeX live, with a draggable 2D / 3D / geometry grapher you can drop into the page, figures, worksheets from your own problems, and one-click PDF export.
Sliders and animation, parametric curves, inequalities, piecewise functions, points of interest on click, tangent lines, derivatives and shaded areas, tables, contour maps, cross-sections, vector fields and tangent planes in 3D — and PNG / TikZ export.
Perpendiculars, parallels, tangents, circumcenter / incenter / centroid / orthocenter and the nine-point circle, reflections, rotations, dilations, intersections, loci, areas and slopes that all update as you drag — and drop straight into a problem.
Write problems with a LaTeX keyboard, publish them to the Courtyard, build takeable tests and worksheets, suggest the Daily challenge, or duel a friend head-to-head on the same problems.
Book-style lessons with a proof of every formula, worked problems, side notes and try-its, practice after every section that saves your place, a Formulas & Methods sheet for every competition — and every course downloads as a printable booklet.
Sixty-two numbered practice contests at real length and timing — 25 questions in 75 minutes for AMC, the Target round in four six-minute pairs, the six-problem USAMO over two days, the Putnam in two six-problem sittings, a generating-function problem on every olympiad set — with official scoring, an answer sheet, arrow-key navigation, full solutions at the end, and every set downloadable as a LaTeX-typeset PDF.
Ascend the castle floor by floor — each level raises the difficulty.
Head-to-head, one problem at a time, against the clock.
Race the clock — solve as many as you can on one life. Starts hard.
Write problems and worksheets with the built-in LaTeX creator, publish them for everyone, and get a feed tuned to the topics you practice. Suggest your best problem as the site's Daily challenge — and download anything as a LaTeX file.
Visit the CourtyardNot sure where to start?
Twelve adaptive questions place you at exactly the right level — no account needed.
Create a free account to save your progress, or jump straight into the problems.