Summarize what the Arquimedes math problem database holds: 1,038,963 problems across 9 datasets, with problem counts by dataset, category, and competition, and written-solution counts by kind. Call it first to learn which category, dataset, and competition values exist before filtering arquimedes_search_problems or arquimedes_sample_problems. Takes no arguments.

Find problems by keyword in 1,038,963 competition and olympiad math problems. Full-text search returns problems whose statement or title contains all the query words: a topic, a theorem name such as 'Cauchy-Schwarz', or a LaTeX fragment. Optional filters narrow by category, dataset, competition, and Mohs difficulty (1.0 to 10.0). Results are summaries (id, title, competition, year, difficulty, answer, statement) without solutions; pass an id to arquimedes_get_problem for solutions and hints. To get random problems instead of keyword matches, use arquimedes_sample_problems.

Draw random problems from 1,038,963 competition and olympiad math problems, uniformly among those matching optional filters: category, dataset, competition, contest year, Mohs difficulty range (1.0 to 10.0), multiple-choice only, or with a diagram. Use it to build practice sets, mock contests, or evaluation samples; pass the same seed to repeat a draw. Results are summaries without solutions; pass an id to arquimedes_get_problem for solutions. To find problems about a specific topic or keyword, use arquimedes_search_problems.

Fetch one problem by its id, as returned by arquimedes_search_problems or arquimedes_sample_problems (e.g. 'prob.ahsme-1950-p10', 'prob.numina-000369'). Returns the full record: LaTeX statement, answer choices, answer, written solutions with progressive hints, difficulty, source, and diagram references. Ids cannot be guessed; an unknown id returns an error, so discover ids with search or sample first.