Editorial · Pathway · Results · Preparation
News & Updates — Editorial Coverage of the UKMT Competition Year
Editorial articles on the British Mathematical Olympiad and the UKMT competition year, written for international students preparing for the senior pathway. Articles are typically 1,500 to 2,500 words and are filed against four standing categories.
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BMO Pigeonhole Principle: Define the Boxes Before Counting the Objects
Learn why BMO pigeonhole proofs fail when students count objects before locking down the partition. A checked worked case, a deliberate misfire, and a diagnostic to fix your combinatorial proof structure. Read article
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BMO Modular Arithmetic: Choose a Modulus That Rules Out an Integer Solution
A worked guide to selecting the right modulus in BMO number theory problems: when modular arithmetic proves no integer solution exists, with checked examples, a contrasting case where the wrong modulus fails, and diagnostic steps for your next practice session. Read article
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SMC to BMO Proof Writing: Replace a Plausible Pattern With a Complete Argument
Transitioning from the Senior Mathematical Challenge (SMC) to the British Mathematical Olympiad (BMO) requires replacing pattern-matching intuition with rigorous, complete written arguments. This guide explains the shift in reasoning demands and provides worked teaching illustrations with checked steps. Read article
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BMO Extremal Principle: Choosing the Largest or Smallest Object to Start a Proof
Mastering the extremal principle is key for BMO proofs. Learn how selecting the largest or smallest object simplifies complex logic, with worked hypothetical teaching illustrations and common pitfalls. Read article
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BMO Equality Cases: Finishing an Inequality Proof Completely
Learn why BMO inequality problems demand explicit equality-case verification, with two worked hypothetical examples, a common shortcut mistake, and a practical diagnostic to check your own proofs. Read article
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BMO Induction: Choosing a Statement Strong Enough to Prove
A focused guide on selecting the correct induction hypothesis for BMO proofs, featuring worked hypothetical examples and diagnostic strategies. Read article
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BMO Registration China: Direct Entry Rules, Centre Finding, and Deadline Planning for 2026
Guide to BMO Round 1 registration in China for 2026. Learn direct entry rules, key deadlines, exam format differences vs AMC, and preparation strategies for proof-based mathematics. Read article
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BMO Infinite Descent: How to Write a Complete Proof
A guide to completing BMO-style infinite descent proofs by choosing a least positive solution, preserving integrality, and proving strict decrease. Read article
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BMO1 Past Papers Solutions: Requesting Worked Answers and Proof Feedback
A practical guide to locating BMO1 past paper solutions, using them without destroying their learning value, and building a personal proof-archive for British Mathematical Olympiad preparation. Read article
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SMC Past Papers Before the 8 October China Sitting: A Day-by-Day Triage Table for the New 22-Plus-3 Format (2026)
Twenty days, five papers, one conversion rule: which SMC past paper to sit on which day before the 8 October China sitting, and how to rehearse the 000-999 questions. Read article