Published onJuly 3, 2026Divisibility by 9 via Digit Sumhsc-mathsextension-2proofsnumber-theorymediumA direct biconditional proof demonstrating that a three-digit number is divisible by 9 if and only if the sum of its digits is divisible by 9.
Published onJuly 3, 2026The Pigeonhole Principle and Leading Digitshsc-mathsextension-2pigeonhole-principlelogarithmshardA guided proof demonstrating that the orbit of an irrational rotation is dense using the Pigeonhole Principle, and proving that there exists a power of 2 starting with 2025.
Published onJuly 3, 2026Sequence Limits and the Squeeze Theoremhsc-mathsextension-2sequenceslimitssqueeze-theoremA challenging HSC Extension 2 Mathematics problem exploring the evaluation of sequence limits using inequalities and the Squeeze Theorem.