ProblemLab

Personalized
competition math.

Start with your own level and goal. ProblemLab builds a customized daily plan from real AMC, AIME, and original problems. When you get stuck, ProblemLab gives you the exact support you need to keep going.

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Free. No experience assumed.

Library index

AMC 10 and AIME problem archive

real sources

Problems

Worked solutions

  • AMC 10A 2014 · #1850

    What is 10⋅(12+15+110)−110\cdot\left(\tfrac{1}{2}+\tfrac{1}{5}+\tfrac{1}{10}\right)^{-1}?

  • AMC 10A 2024 · #1850

    What is the value of 9,901⋅101−99⋅10,1019,901\cdot101-99\cdot10,101?

  • AMC 10 2000 · #201515

    Let AA, MM, and CC be nonnegative integers such that A+M+C=10A+M+C=10. What is the maximum value of A⋅M⋅C+A⋅M+M⋅C+C⋅AA\cdot M\cdot C+A\cdot M+M\cdot C+C\cdot A?

Open event · try it nowrated 1150

At a party, each of the 88 guests shakes hands exactly once with every other guest. How many handshakes occur?

How your training works

01

Placement

Seven problems, adaptive difficulty. A few minutes later you have a rating on the same 600-1800 scale every problem in the library is graded on.

02

The daily card

Your plan posts a short card of problems each day, picked for your level and your goal contest, with review days built in.

03

The climb

Every answer moves your rating. Stuck means a hint that nudges, a worked solution, then a topic video. The plan rebuilds itself as you improve.

An open mathematics study observatory overlooking a landscape of geometric paths.

A place to work the problem all the way through.

Start with one honest placement. Then take a daily route through real contest problems, with a plan that changes as you do.

Start your placement

Forty-three years of real contests

Every problem carries its source, its difficulty on the shared rating scale, and its topic. When one beats you, a worked solution and a topic video are one click away. Hard problems come with two solutions.

Browse the full library after placement →

AMC 10

2000 – 2025

1,021

AIME

1983 – 2025

929

ProblemLab originals

with full solutions

27

Topics from linear equations to modular arithmetic, tagged on 24 skills

Preview · after a miss on AMC 10A 2019 #17

Case 1: the red cube is excluded. Arranging one red, three blue, and four green cubes gives 8!4!⋅3!=280\frac{8!}{4!\cdot 3!}=280 arrangements…

Shown after solving: two worked solutions + a casework video

Missing a problem is the useful part

A wrong answer opens two steps: a worked solution — written by the AoPS community, not the contest itself — then a short video on the exact skill the problem tested. A hint is there before you answer, and it nudges without spoiling.

A geometric learning path crossing a bright landscape toward an open research pavilion.
ProblemLab

Every hard problem is a place to begin.

The placement test takes just a few minutes.

Take the placement test