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AMC counting techniques problems

Complementary counting, inclusion-exclusion, bijections, recursion and the pigeonhole principle.

141 problems in the archive use these ideas — 76 from the AMC 10 and 65 from the AMC 12.

Picks a problem you have not seen, at about the difficulty you are handling.

60 most recent problems

Newest contests first. Every problem opens with its answer choices, hints and a worked solution.

Use Start counting techniques practice above to keep going through the remaining 81, or browse them by contest in the AMC 12 and AMC 10 archives.

Back to all counting & probability problems.