Train your brain, one clever problem at a time
Original competition & Olympiad-style problems for every grade. Each task teaches a named abstract-thinking strategy — the same reasoning skills the SAT and math competitions reward. Pick your grade:
Grade 1 · 2 · 3 · 4 · 5 · 6 · 7 · 8 · 9 · 10 · 11 · 12
Every puzzle has its own page
Browse without the app: each grade has a page with all its puzzles, hints and solutions, and every puzzle has its own page to share or print.
Grade 1 · 12 puzzles
All grade 1 puzzles on one page
- Puzzle 1: Spot and count repeating groups
- Puzzle 2: Act it out step by step
- Puzzle 3: Draw a picture
- Puzzle 4: Order by comparing (transitivity)
- Puzzle 5: Check every possible case
- Puzzle 6: Guess and check smartly
- Puzzle 7: Simulate — and watch the ending
- Puzzle 8: Sort into cases and check a limit
- Puzzle 9: Track two patterns at once
- Puzzle 10: Track neighboring pairs
- Puzzle 11: Working backwards
- Puzzle 12: Symmetry
Grade 2 · 12 puzzles
All grade 2 puzzles on one page
- Puzzle 1: Count both ends in two groups
- Puzzle 2: Multiplication with equal groups
- Puzzle 3: Do the experiment in your head
- Puzzle 4: Connect ages across a timeline
- Puzzle 5: Swap and cancel on balances
- Puzzle 6: Compare two landing trails
- Puzzle 7: Beware of double counting
- Puzzle 8: Find the rate first
- Puzzle 9: Infer and test an addition rule
- Puzzle 10: Check two conditions
- Puzzle 11: Working backwards
- Puzzle 12: Extreme cases
Grade 3 · 12 puzzles
All grade 3 puzzles on one page
- Puzzle 1: Build greedily, digit by digit
- Puzzle 2: Bridge through a round number
- Puzzle 3: Compare two orders using a shared starting point
- Puzzle 4: Label with a letter (early algebra)
- Puzzle 5: Work backwards
- Puzzle 6: Systematic listing
- Puzzle 7: Bounding an extreme by ordering
- Puzzle 8: Eliminate using odd and even numbers
- Puzzle 9: Find the missing change
- Puzzle 10: Count in separate cases
- Puzzle 11: Parity
- Puzzle 12: Symmetry (mirror pairs)
Grade 4 · 12 puzzles
All grade 4 puzzles on one page
- Puzzle 1: Compare two expressions by their differences
- Puzzle 2: Pieces vs. cuts
- Puzzle 3: Combine moves, then discard full laps
- Puzzle 4: List factor pairs, then test
- Puzzle 5: Restore a missing area
- Puzzle 6: Count the gaps, not the posts
- Puzzle 7: Start from the extreme
- Puzzle 8: Count digit occurrences by position
- Puzzle 9: Test a pattern against examples and counterexamples
- Puzzle 10: Find and add gaps to a common total
- Puzzle 11: Pigeonhole principle
- Puzzle 12: Invariants
Grade 5 · 12 puzzles
All grade 5 puzzles on one page
- Puzzle 1: Compare to a benchmark
- Puzzle 2: Compare two division sentences
- Puzzle 3: Count shared endpoints and gaps
- Puzzle 4: Count overlapping groups using totals
- Puzzle 5: Sort by position, then count
- Puzzle 6: Use place-value structure
- Puzzle 7: Track two piles backward
- Puzzle 8: Block-swap pairing with a leading-zero check
- Puzzle 9: Increasing-step pattern
- Puzzle 10: Equal grouping from chart totals
- Puzzle 11: Extreme cases
- Puzzle 12: Parity
Grade 6 · 12 puzzles
All grade 6 puzzles on one page
- Puzzle 1: See percents as fractions
- Puzzle 2: Move along the number line
- Puzzle 3: Halfway = average
- Puzzle 4: Compare shares of an unchanged total
- Puzzle 5: The middle is the average
- Puzzle 6: Test with easy numbers
- Puzzle 7: Filter square roots using remainders
- Puzzle 8: Assume and find a contradiction
- Puzzle 9: Reasoning with digit place values
- Puzzle 10: Compare pair averages using totals
- Puzzle 11: Symmetry
- Puzzle 12: Invariant (conserved cubes)
Grade 7 · 12 puzzles
All grade 7 puzzles on one page
- Puzzle 1: Undo a repeated routine in reverse
- Puzzle 2: Find a last-digit cycle
- Puzzle 3: Use a full-turn invariant
- Puzzle 4: Percents multiply, not add
- Puzzle 5: Build a count, then correct for overlap
- Puzzle 6: Total distance ÷ total time
- Puzzle 7: Count guaranteed prime factors
- Puzzle 8: Count unordered groups by dividing out their orders
- Puzzle 9: Find and verify a two-term recursive pattern
- Puzzle 10: Compare signed triangular areas
- Puzzle 11: Bound with neighboring pairs
- Puzzle 12: Pigeonhole principle
Grade 8 · 12 puzzles
All grade 8 puzzles on one page
- Puzzle 1: Split side lengths around their midpoint
- Puzzle 2: Recognize structure (triples)
- Puzzle 3: Use a common power for squares and cubes
- Puzzle 4: Relate proportional rise and run
- Puzzle 5: Use a shared root and factor pairs
- Puzzle 6: Count arrangements and ties
- Puzzle 7: Track prime exponents
- Puzzle 8: Checkerboard coloring and construction
- Puzzle 9: Count two interleaved sequences
- Puzzle 10: Extremal reasoning with reordered increases
- Puzzle 11: Counting the complement
- Puzzle 12: Double counting
Grade 9 · 12 puzzles
All grade 9 puzzles on one page
- Puzzle 1: Check zero factors before canceling
- Puzzle 2: Compare trips to find a unit rate
- Puzzle 3: Cancel even terms at opposite inputs
- Puzzle 4: Concurrency with a distinctness check
- Puzzle 5: Factor to find a remainder
- Puzzle 6: Factor a difference of squares
- Puzzle 7: Factor a difference of squares and count symmetric solutions
- Puzzle 8: Link symmetric expressions through identities
- Puzzle 9: Place-value equations and divisibility
- Puzzle 10: Balance a product
- Puzzle 11: Count by blocks and gaps
- Puzzle 12: Pairing odd-degree vertices
Grade 10 · 12 puzzles
All grade 10 puzzles on one page
- Puzzle 1: Complete the square
- Puzzle 2: Compare linear and quadratic scaling
- Puzzle 3: Convert an area ratio into a length ratio
- Puzzle 4: Choose a perpendicular direction using a half-plane
- Puzzle 5: Cofunction pairing and double-angle identity
- Puzzle 6: Double counting in a triangulation
- Puzzle 7: Parity of prime factors in divisor counts
- Puzzle 8: Track two interacting cycles
- Puzzle 9: Recognize alternating ratios and compare prime exponents
- Puzzle 10: Weighted conditional probability
- Puzzle 11: Permutation parity via inversions
- Puzzle 12: Exchange argument
Grade 11 · 12 puzzles
All grade 11 puzzles on one page
- Puzzle 1: Use equal spacing to recover exponential growth
- Puzzle 2: Translate logarithms into exponents
- Puzzle 3: Quadratic finite differences
- Puzzle 4: Compare discriminants and count distinct roots
- Puzzle 5: Geometric series with overlapping sets
- Puzzle 6: Complete the random order and use symmetry
- Puzzle 7: Inclusion–exclusion with rotational symmetry
- Puzzle 8: Bridge between symmetric identities and an attainable bound
- Puzzle 9: Factor an integer polynomial using known roots
- Puzzle 10: Combine modular cycles with exponent divisibility
- Puzzle 11: Find a grouped parity invariant
- Puzzle 12: Coordinate normalization
Grade 12 · 12 puzzles
All grade 12 puzzles on one page
- Puzzle 1: Compare squares to reveal a complex number’s real part
- Puzzle 2: Track a composition around a cycle
- Puzzle 3: Use a zero-sum identity for cyclic differences
- Puzzle 4: Split into regions, then verify roots
- Puzzle 5: Symmetrize reciprocal log products
- Puzzle 6: Count cyclic arrangements using gaps and rotational symmetry
- Puzzle 7: Pell-equation descent
- Puzzle 8: Polynomial reduction and interpolation
- Puzzle 9: Classify with modular arithmetic
- Puzzle 10: Conditional counting by cases
- Puzzle 11: Binary factorization modulo 2
- Puzzle 12: Unfolding by reflection
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