Challenge Problems - Yr 4-7. Variety of topics including fractions, decimals, algebra, probability.
Open the Combination Lock - Yr 5+. Logic puzzle.
Factor graph puzzle - Yr 5+. Knowledge of factors.
Factor family puzzle - Yr 5+. Knowledge of factors.
Intermediate Olympiad style puzzles - Yr 7+. Prime factorisation, alphametics, probability.
Dart board puzzle - Yr 7+. Knowledge of divisibility, primes, probability.
Fun quick alphametic - Yr 7+. Knowledge of divisibility and factorisation.
Cool bases puzzle - Yr 7+. Algebra, bases.
Coin flipping puzzles - Yr 7+.
Sequences question - Yr 7+. Algebra.
Bases: squares and cubes problem - Yr 7+. Algebra, knowledge of bases, divisors. Cases.
Smallest integer satisfying this property - Yr 7+. Knowledge of divisibility, prime factorisation, remainders.
Units digit problems - Yr 7+. Mod, bases, factorials.
Prime decomposition problems - Yr 7+. Basic number theory.
Divisibility and powers - Yr 7+. Modular arithmetic.
1089 puzzle - Yr 8+. Fairly short. Algebra, place value, cases.
Perfect squares puzzle (slightly shorter) - Yr 8+. Cases. NEEDS CLEANUP!
Fairly short alphametic - Yr 8+.
ABCDE puzzle - Yr 8+. Fairly short. Algebra, place value, cases.
Grouping the integers - powers of 2 puzzle - Yr 8+. Fairly short. Algebra, place value, cases.
Perfect squares puzzle (LONG) - Yr 8+. Cases. NEEDS CLEANUP!
Make this a cube - Yr 8+. Knowledge of algebra, prime factorisation.
Mod powers puzzle - Yr 9+. Knowledge of index laws, mod.
Tough number theory problem - Yr 9+. Divisibility, difference of squares, exponents. Cases.
For how many integers is this fraction a square? - Yr 9+.
Nines puzzle - Yr 9+. Knowledge of mod.
Problems using the Sophie Germain identity - Yr 9+. Primality, geometry, series.
Probability that a certain power has a certain units digit - Yr 9+. Knowledge of index notation, mod, probability basics.
Which base? - Yr 10+. Knowledge of bases, quadratics.
Find the base - Yr 10+. Knowledge of quadratics.
Units digit of a sum of factorials - Yr 10+. Knowledge of factorial notation.
Reversing digits puzzle - Yr 10+. Knowledge of algebra (including differences of squares), prime factorisation.
Quick base question - Yr 10+. Knowledge of quadratics.
Unknown base - Yr 10+. Knowledge of bases, index laws.
Primes puzzle - Yr 10+. Number theory question, requires basic knowledge of primes and divisibility.
Multiple bases - Yr 10+. Knowledge of bases and simultaneous equations.
Show that this equation has no solution - Yr 10+. Quadratic, modular arithmetic.
Proving a number is composite in any base - Yr 10+. Factorisation, difference of squares.
Fairly short proof by contradiction - Yr 10+. Parity.
Divisibility by 33 puzzle - Yr 10+. Mod, exponents.
Product of four consecutive numbers can't be square - Yr 10+.
Recurrence relations applied to a trig problem - Yr 11+. Trig identities. Tough problem - recurrence relation will need explanation.
Find a function with f(f(n))=-n - Yr 11+. Definition of a function, piecewise function.
Decimals in other bases - Yr 11+. Bases, summation notation, geometric series.
Fractions in other bases - Yr 11+. Bases, summation notation, geometric series.
Lagrange Identity problems - Yr 11+.
Functional Equations - Yr 11+.
Stars and threes alphametic - Cases.
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