Pathway C
Competition Mathematics™
Develop strategic non-routine problem solving through AMC pathways, number theory, geometry, combinatorics, probability, logic, and mathematical ingenuity.
AMC 8
Middle-school competition covering number theory, counting, geometry, probability, and logic.
AMC 10
Advanced reasoning in algebra, geometry, number theory, and combinatorics up to Grade 10.
Math Kangaroo
International problem-solving contest emphasizing clever, accessible reasoning.
Olympiad & Original
Proof-based olympiad reasoning plus original MathGymUSA.ai competition problems.
Competition problem library
CompetitionApproachable
The Locker Problem
1000 lockers, all closed. Student 1 opens all; student 2 toggles multiples of 2; student 3 toggles multiples of 3… After 1000 students, which lockers remain open and why?
Number theoryDivisibility
CompetitionChallenging
Sum of Digits Cycle
Find the last two digits of 7⁷⁷. Then determine the last digit of the result of that computation — a tower of exponents.
Modular arithmeticAMC 10
CompetitionOlympiad
Counting Triangulations
In how many ways can a convex (n+2)-gon be triangulated? Discover the Catalan numbers and prove the recurrence.
CombinatoricsCatalan
AMC 8
Competition connection
Combinatorics — Counting with cases, the multiplication principle, and complementary counting appear in nearly every AMC 8.
How many 3-digit numbers have digits that strictly increase?
AMC 10
Competition connection
Geometry — Angle chasing, similar triangles, and area methods are the backbone of AMC 10 geometry.
Two circles of radius 5 are externally tangent. Find the area between them enclosed by their common external tangents.