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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BMO1 Diophantine equations: factor or bound? A decision table for two-variable proofs
BMO1 Diophantine equations need a structural decision: factor a product form or bound a variable. This guide gives a decision table, a complete positive-integer factor-pair audit, and a finite-range bound check. Read article
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BMO1 angle chasing: a configuration audit before you add an auxiliary circle
Before adding an auxiliary circle in a BMO1 angle chase, record which side of each chord the key points lie on, the order of points on each line, and whether the quadrilateral is convex or crossed. Equal angles alone are not enough: same-side equal angles support concyclicity; opposite-side equal angles generally do not. Read article
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BMO2 inequalities: Cauchy-Schwarz, AM-GM or substitution? A pre-write diagnostic
A pre-write diagnostic for BMO2 inequalities: choose AM-GM, Cauchy-Schwarz or substitution by domain, structure and attainable equality, then write a complete proof. Read article
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BMO2 Qualification China: What the 2026 Seven-Point Line Means for 2027
China’s reported BMO2 qualification line for the 2026 cycle was 7 points on Round 1’s 60-mark paper — a China-specific entry threshold, separate from the award reference lines and from the UK top-100 route. Here is what that number does and does not imply for the January 2027 round. Read article
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SMC results 2026: official 71/54/41 awards and Hanlin tally as China BMO1 deadline nears
The live UKMT awards page confirms 2026 SMC Gold 71+, Silver 54+, Bronze 41+ and BMO1 qualification 101+ subject to eligibility. Hanlin’s 27 October report lists 19 gold, 9 silver and 4 bronze among coached and registered entrants, including one 125 full mark. Read article
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BMO Trigonometry: When a Geometry Proof Needs Sine Rule Before an Auxiliary Line
For BMO geometry proofs involving side ratios in adjacent triangles, apply the sine rule before adding auxiliary lines. This guide explains when to use metric trigonometry versus circle or line constructions. Read article
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BMO Graph Theory: When to Model a Problem with Vertices and Edges
For the 2026-27 BMO preparation season (BMO1 on 19 November 2026, BMO2 on 21 January 2027 in the China region), a BMO1 or BMO2 candidate who sees a combinatorics problem about people, pairs, connections or forbidden configurations should ask three questions before reaching for casework: is the relation binary, is the target a triangle or… Read article
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BMO Combinatorics Recurrence: How to Build the State Before Counting
When direct counting fails in BMO-style problems, use a recurrence-first method. Define states, identify moves, and prove exhaustiveness with this teaching illustration. Read article
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BMO Geometry Auxiliary Construction: Choosing Between Circle and Line
Stuck on a BMO1 geometry proof? Learn when to introduce an auxiliary circle for angle chasing versus an auxiliary line for ratios and similarity. Read article
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BMO Functional Equations Substitution: Systematic Checks for Complete Proofs
Spotting one solution is not enough. This guide provides systematic substitution checks to turn lucky guesses into complete ‘determine all functions’ proofs for BMO candidates. Read article