P·01
AMC 8
Foundations of contest thinking
Number sense, clever counting, geometric intuition. Contest problems are puzzles with structure you can find.
Institute of Competition Mathematics
Learn competition mathby solving, not watching.
One continuous curriculum from AMC 8 to advanced problem solving. Interactive lessons that gate on understanding, adaptive practice, scored mock contests, and a Socratic AI coach that hints but never hands you the answer.
PATHAMC 8→AMC 10/12→AIME→USAMTS→Problem Solving
Built for the full climb
58 lessons1000+ original problems6 contest tracksFree to start
§ 01 · Programs
Six programs.
One trajectory.
Every program is a stage of the same climb, from first principles to the edge of pre-college math.
P·02
AMC 10/12
Speed, precision, depth
Algebraic technique, combinatorial identities, and trigonometry executed cleanly under time pressure.
P·03
AIME
Where problems become puzzles
Multi-step problems demanding synthesis across domains. We train the decomposition instinct: reduce, transform, conquer.
P·04
USAMTS
The art of proof
Take-home, untimed rounds argued with complete rigor. The talent-search format that rewards a clean write-up over a fast guess.
P·05
Problem Solving
Standardized test math
SAT and ACT-style math, built on the same reasoning habits, just aimed at a different clock.
P·06
Advanced Problem Solving
Beyond the syllabus
For students who have finished the core curriculum. Open-ended, non-routine problems with no labeled method and no single right approach.
§ 02 · The Lucid Method
Reasoning is
a discipline.
Five stages, in strict logical order. Each one is a prerequisite for the next, like lemmas building toward a theorem.
Lemma 1
Foundations
School mathematics rebuilt from first principles, so nothing is memorized that can instead be derived.
Lemma 2
Pattern Recognition
Invariants, symmetry, extremal cases, parity. The instinct that turns a blank page into a plan.
Lemma 3
Proof Writing
From intuition to rigor. Write, critique, rewrite, until precision becomes second nature.
Lemma 4
Creative Problem Solving
Non-routine problems with no labeled method. You build the approach yourself, from nothing.
Theorem
Timed Competition Practice
Full simulations under authentic constraints, then forensic review of every decision.
§ 03 · Why Lucid
Built differently.
No cohort to keep up with, no coach to schedule around. Just you, the curriculum, and an AI that won’t let you fake understanding.
100% virtual, always on
Every lesson, problem, and mock contest lives on the platform. Log in whenever you have twenty minutes. No seat to book.
Coached, not lectured
The AI coach asks before it answers. Socratic hints, never the final answer.
One continuous curriculum
Six programs, one trajectory. AMC 8 through advanced problem solving, each stage a prerequisite for the next.
Priced like software
Plans start at $5/month. A virtual platform shouldn’t cost what an hour of private tutoring does.
§ 04 · Pricing
Choose your intensity.
Every tier includes the full curriculum platform, problem bank, mock contests, and the AI coach.
Starter
Free
- Full curriculum platform: lessons, bank, contests
- AI coach, Socratic hints on every problem
- Monthly mock competition, scored
- Progress tracking & mastery roadmap
Most chosen
Plus
$5/month
- Everything in Starter
- Unlimited AI coach access
- Weekly mock competitions, scored
- Written solutions to every problem
- Full progress analytics
Pro
$10/month
- Everything in Plus
- Priority AI coach, deeper proof review
- Competition-day strategy guides
- Early access to new content
§ 05 · FAQ
Open questions.
Students in grades 5–12 who want to compete seriously in mathematics, from first-time AMC 8 entrants to students deep into AIME and USAMTS prep. Ambition matters more than current level. We place you by trajectory, not trophy case.
With the free platform. The adaptive engine looks at reasoning habits, not just syllabus coverage, and finds the right entry point. No placement test anxiety.
Nothing here is passive. Every lesson mixes guided discovery, worked examples, and inline checks that gate your progress. You can't just scrub to the end.
Entirely self-paced and 100% virtual. No cohort to keep up with, no seat to book. Everything's on the platform whenever you are, and the AI coach is there the moment you get stuck.
Four to eight hours a week, depending on tier. You learn competition math by struggling with problems, not by watching solutions. The platform sharpens that struggle. It doesn't replace it.
§ 06 · Q.E.D.
Start with one problem.
The full curriculum, problem bank, and AI coach are open. Free to start, no card required.