Published onJuly 3, 2026Irrationality of $\sqrt{2} + \sqrt{3} + \sqrt{5}$hsc-mathsproofshardA hard difficulty HSC math problem on irrationality of $\sqrt{2} + \sqrt{3} + \sqrt{5}$ with full step-by-step solutions.
Published onJuly 3, 2026Irrationals Between Any Two Rationalshsc-mathsproofshardA hard difficulty HSC math problem on irrationals between any two rationals with full step-by-step solutions.
Published onJuly 3, 2026Nested Radicals and a Cosine Formulahsc-mathsproofshardA hard difficulty HSC math problem on nested radicals and a cosine formula with full step-by-step solutions.
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, 2026Power Difference Divisible by x Minus yhsc-mathsproofshardA hard difficulty HSC math problem on power difference divisible by x minus y with full step-by-step solutions.