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Tag: Olympiad Combinatorics
All BMO and UKMT Pathway Guide editorial articles matching this filter. Browse the full archive at News & Updates, or use the navigation to filter by stage, paper, or topic tag.
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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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The BMO1 Number Theory and Combinatorics Toolkit: Parity, Invariants, Pigeonhole and the Right Modulus
Parity, invariants, pigeonhole and choosing the right modulus: how to make BMO1 number theory and combinatorics systematic instead of a matter of luck. Read article