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.

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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