A clean algebraic proof that if n is composite then 2ⁿ − 1 is also composite — establishing that prime exponents are necessary (though not sufficient) for Mersenne primality.
A two-player number game where the first to call 50 wins. Backward induction reveals that winning positions are exactly those congruent to 6 (mod 11).
Three complementary proofs that the number of unordered pairs from n distinct elements equals C(n,2) = n(n−1)/2: a concrete table, a row-sum formula, and the division principle.
A combinatorial count of all distinct triangles in a regular pentagon with its inscribed pentagram, using vertex-type classification and 5-fold rotational symmetry.
A personal ledger of principles across body, mind, profession, money, and relationships.
A meditation on why the AI age may favor those who pursued knowledge for its own sake — and why the ancient love of useless pursuits may prove our most durable advantage.
A framework for better software documentation: gather independent perspectives from product manager, engineer, tester, and writer to surface hidden discrepancies and achieve genuine alignment.
A practical guide to diagnosing pod failures in Kubernetes: checking status, reading logs, executing commands inside containers, and using ephemeral debug containers.
A critical review of BrowserStack’s documentation: nitpicks on minimalism, heading style, admonition misuse, unnecessary images, and site UX — compared against a competitor.
A tutorial on automating browser tests with Python and Selenium, running them at scale on BrowserStack, and wiring up GitHub Actions for continuous testing.
A walkthrough of tic-tac-toe strategy: why perfect play always ends in a draw, and how to exploit imperfect opponents.
A step-by-step tutorial on building a landmark detection application with Python, Google Cloud Storage, and the Vision API.
A concise comparison of REST and SOAP web service architectures — their trade-offs, ideal use cases, and a practical decision guide.
A code review of a Java method that counts needle-string occurrences in a haystack, with API documentation and concrete suggestions for efficiency and clarity.
