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HKIMO 2026 THPT (Grades 10–12 shared) National Final (Heat) Set 05 Question 1

HKIMO · HKIMO 2026 THPT (Grades 10–12 shared) National Final (Heat) Set 05

Question 1

A box has $2015$ balls, each red, green, blue, yellow or black. Any draw of $1800$ balls guarantees at least one of each colour. What is the minimum number to draw to guarantee at least three different colours?

Editorial working convention: Draw without replacement; seek the worst-case guarantee from the stated information.