The Bebras Challenge tests computational thinking — reasoning about problems the way a computer scientist does — without requiring any programming. Over a full term we built those tools from first principles: logic and fallacies, proof techniques, abstraction, graph theory and binary, threaded throughout with real Bebras problems and a recurring "fallacy of the day".
Introduced why the edition focuses on maths and computer science, emphasising problem-solving and persistence over memorisation, and defined the core skills: decomposition, pattern recognition, generalisation, logic and algorithms. Covered a range of logical fallacies (ad hominem, false dichotomy, bandwagon, appeal to authority, post hoc, slippery slope) and first example Bebras problems.
Defined proof as the opposite of a fallacy, contrasting valid inference with false-premise reasoning. Taught proof by contradiction through a seating puzzle, introduced parity as a companion tool, and explored cryptarithms (verbal arithmetic), setting the Seven Bridges of Königsberg as homework.
Worked through Euler's solution to the Seven Bridges problem as a study in abstraction and generalisation, using transport maps to show geographic vs schematic representation. Students followed Euler's method to reach the proof that the walk is impossible — the spark that created graph theory and Eulerian paths.
Defined abstraction as representing only essential features, then contrasted emotion with rationality and classical vs behavioural economics. The core activity was a series of escalating trolley-problem thought experiments, each asking students to separate what matters from the noise.
Introduced graphs (vertices, edges, weights, direction) via an offshore-pipeline design problem. Taught Kruskal's minimum-spanning-tree algorithm and Dijkstra's shortest-path algorithm, with applications from airline scheduling to Sudoku as graph colouring.
Consolidated logic, proof techniques and graphs, then worked three Bebras problems: backtracking on a directed graph, a minimum vertex cover solved by abstraction and contradiction, and a hashing problem contrasting hash lookup with slow linear search.
Recapped the toolkit and introduced the false-compromise fallacy (truth isn't always in the middle). Explained the UK Bebras format in detail — age groups, A/B/C question categories, positive and negative marking and the 45-point starting score — with worked score examples.
Showed how corrupted messages can be detected, then built binary encoding from the ground up: numeral systems, assigning numbers to letters (ASCII), zero-padding and positional notation, including a curiosity sidebar on why any number to the power 0 equals 1.
Had students devise a decimal-to-binary conversion algorithm, took on numerology as the fallacy of the day (spurious correlations and post hoc reasoning), then introduced error detection via the parity bit with even/odd worked examples.
Reviewed parity-bit decoding and the class's Bebras results, then explored what computing is and what comes next: the Bebras Coding Challenge (Blockly vs text), the Perse Coding Challenge with a C# solution, and the British Informatics Olympiad.
Introduced programming as sequenced instructions and control flow — if/else, "repeat N times" and "repeat forever" — and the event loop behind everyday apps. Mapped the layers from hardware and machine code up to languages and block tools, with a loop exercise drawing a circle.
Framed spreadsheets as programs, mapping cells to variables, data types and functions (SUM, AVERAGE). Covered absolute references and multi-sheet tricks, then ran hands-on projects building a times table and an age calculator, closing with a feedback survey.
