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The seven levels

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Climb seven levels to reach Disentis. Each level has seven adventures of ten problems. Seven adventures finished at a level open the next one. The basics are learned with STELLA, our tutoring academy; here your child uses them on real challenges. Between adventures, Base Camp is where you train on a level’s problems: fresh ones made on the spot, as many as you like, each one met adding a stone to that level’s cairn. Adventures move the Ei; Base Camp moves the Stones. Levels 1 to 5 hold real pools of problems, and every adventure is a fresh set of ten; the rest of the mountain is still in the clouds. The Euler Index, explained →

For parents and teachers: the topics and skills at each level

What a child is assumed to know at each level, condensed from the Euler100 Level Definitions (draft of 4 October 2026). Ages are a guide, never a gate: a child plays the level they have reached.

  1. Level 1 · Explorer (from age 8; most children are comfortable at 9)
    Topics: Number, patterns, shape, measurement and data.
    Skills: Counting a drawn arrangement by rows and groups; adding and subtracting with meaning within 100; small multiplication facts as groups; halves, doubles and quarters of a pictured whole; reading a pictogram, a ruler, a number line and a clock to the half hour; a shape turned, flipped or mirrored; a balance that means equal; continuing a repeating pattern. Every problem is a picture read before anything is computed.
  2. Level 2 · Adventurer (from age 9; most children are comfortable at 10)
    Topics: Number, fractions in pictures, measurement, shape and data.
    Skills: Tables to 10 × 10; division with a remainder and what the remainder means; reading a calculator’s decimal as “six and a bit”; perimeter as a walk and area by counting squares; which net folds to a cube; a reflection or quarter-turn on a grid; bar charts and two-attribute tables; unit rates (“one costs 3, four cost 12”); “three times as many” against “three more”; a pattern’s rule in words; running a two-step rule forwards and undoing it; elapsed time.
  3. Level 3 · Alphinest (from age 10; most children are comfortable at 11)
    Topics: Number structure, fractions and percentages, geometry, ratio and counting.
    Skills: Factors, multiples and primes to 100; divisibility by 2, 5 and 10 by eye; fraction notation and equivalence; a fraction of a quantity; decimals to two places; 10, 25 and 50 per cent as a tenth, a quarter and a half; areas of rectangles and composite shapes; a right-angled triangle as half a rectangle; 90, 180 and 360 degrees; volume by counting cubes; coordinates; scaling a recipe; ratio in words drawn as bars; “for each of these, each of those” on a drawn tree; reading a timetable.
  4. Level 4 · Aviator (from age 11; most children are comfortable at 12)
    Topics: Number structure, ratio and percentage, geometry and angles, patterns to the nth case.
    Skills: Prime factorisation; highest common factor and lowest common multiple; divisibility rules for 2, 3, 5, 9 and 10; odd and even under addition and multiplication; remainders as labels; ratio a:b and sharing in a ratio; percentage of a quantity; area of a triangle and a parallelogram; angles on a line, at a point and in a triangle; the mean as a fair share; the 2027th term of a pattern. A letter may stand for an unknown, never required.
  5. Level 5 · Astronaut (from age 12 (11 for the exceptional child); comfortable at 13)
    Topics: Rates and proportion, early algebra, probability, angles and area, number cycles, games.
    Skills: Negative numbers in context; journeys — distance, time and how fast — and other compound rates; direct and inverse proportion; percentage change; one-step equations, algebra permitted but never required; probability as a fraction of equally likely outcomes; the mean from totals (and why an average of averages is a trap); angles on parallel lines and polygon angle sums; area ratios of triangles; circumference and circle area with π supplied; remainders as cycles; a game position as winning or losing.
  6. Level 6 · Stellar (from age 12; comfortable at 13 — the top band of a strong national junior cohort)
    Topics: The same topics as Level 5, with no scaffolding.
    Skills: No new vocabulary: the absence of hints is the level. Parity and two-colour arguments, pigeonhole with natural boxes, small cases that build to a rule, elementary number theory with 3, 9, 11 and squares, the basic angle facts — used unprompted and combined, with “find the most and show it can be done” as the signature. Being calibrated with the first Level 6 pool.
  7. Level 7 · Genius (13 and under)
    Topics: The junior olympiad repertoire, numeric answers only.
    Skills: The extremal principle, double counting, quantities that only ever move one way, counting under symmetry — composed without a worked strip of small cases, never a written proof. The summit, and Disentis. Set with the Level 6 calibration.
LEVEL 1

Explorer

First steps on the mountain: patterns, sums and the joy of ?
opens with your child’s login
LEVEL 2

Adventurer

Further up the valley
After 7 at Explorer
LEVEL 3

Alphinest

The high nest above the treeline
After 7 at Adventurer
LEVEL 4

Aviator

Where the air gets thin
After 7 at Alphinest
LEVEL 5

Astronaut

Leaving the map behind
After 7 at Aviator
LEVEL 6

Stellar

Navigating by the stars
After 7 at Astronaut
LEVEL 7

Genius

The summit, and Disentis
After 7 at Stellar

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