Levels 1–2
Foundation
Recall a fact or apply one familiar procedure.
The route is visible. Your main job is accurate execution and clear notation.
Goal: Build fluency, confidence, and dependable fundamentals.
Pick the right challenge. Set the right pace.
Difficulty tells you how much reasoning a problem asks for. A time limit changes how you practice that reasoning. Use both with intention—not as a verdict on your ability.
A scale for the reasoning, not the person.
The ten levels form five useful bands. Your best level can vary by subject, and that is completely normal.
Levels 3–4
Developing
Connect a few steps or decide which standard method fits.
You may need to organize information, compare approaches, or choose a useful representation.
Goal: Practice method selection instead of relying on an obvious cue.
Levels 5–6
Proficient
Coordinate several ideas or find a strategic reduction.
The individual tools are familiar, but recognizing how they work together is the challenge.
Goal: Strengthen flexible problem solving and multi-step reasoning.
Levels 7–8
Advanced
Reveal hidden structure and synthesize advanced ideas.
False starts are normal. A non-obvious observation often unlocks the rest of the solution.
Goal: Develop persistence, conjecture-making, and proof control.
Levels 9–10
Expert
Build an original route through an exceptional challenge.
The key insight may be highly problem-specific, and a complete solution can require several deep ideas.
Goal: Explore at the edge of your current understanding without expecting a quick finish.
A useful session is usually mixed. Start below your target level to warm up, spend most of your time at the target, and finish with one stretch problem above it.
Choose a clock that matches the goal.
These per-problem ranges are starting points, not pass/fail rules. Proofs, unfamiliar topics, and higher levels often need more time.
A dependable default
Try 10–15 minutes for a focused attempt. If the method is still unclear, record what you tried, learn from the solution, then return to the problem later.
UntimedLearn
Best for a new topic, a difficult stretch problem, or writing a complete explanation.
20–30 minExplore
Enough room to test ideas, recover from a false start, and check a multi-step solution.
10–15 minFocus
A balanced default when you want steady progress with gentle time pressure.
3–5 minSprint
Useful for recall and routine work—not for judging your ability on an insight-heavy problem.
What success looks like at different times
A timer can limit the attempt without lowering the value of the practice.
| Time budget | Good match | A productive outcome |
|---|---|---|
| 3–5 minutes | Levels 1–2 | Finish accurately; on Levels 3–4, identify a promising method. |
| 10–15 minutes | Levels 2–5 | Complete and check routine work; make a purposeful start on Levels 5–6. |
| 20–30 minutes | Levels 4–7 | Solve, explain, and verify—or develop a sustained approach to a harder problem. |
| Untimed | Any level | Learn deeply, compare methods, and write a solution you could teach. |
A little more context.
Is a difficulty level the same as a school grade?+
No. The level describes the reasoning burden of the problem, not the age or grade of the solver. A problem can use elementary content and still be difficult because the useful idea is well hidden.
Why can two problems at the same level feel very different?+
Your experience varies by subject. You might recognize Level 6 algebra patterns quickly but need much longer on Level 6 geometry. Treat the level as a shared reasoning benchmark, then adjust for your own strengths.
Does a longer solution always mean a harder problem?+
Not necessarily. A long solution may contain routine calculation, while a short solution may depend on one difficult insight. The level is based mainly on the hardest reasoning step in a reasonably discoverable solution.
Should every practice session use a timer?+
No. Untimed work is usually better while learning a technique or studying a hard problem. Add a timer when your goal is recall, method selection, pacing, or making decisions under pressure.
What should I do when time runs out?+
Pause before opening the solution. Write down what you know, the approaches you tried, and the exact point where you got stuck. Then compare that work with the solution and retry the key step without looking.
When should I move to a harder level?+
Move up when you can solve several problems at your current level with sound reasoning—not just recognize one repeated pattern. Keep some easier work for fluency and add one or two stretch problems at the next level.
Choose a level, then stay curious.
Use the filters to find a problem that fits today’s goal. You can always change the level or remove the timer next time.