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HKIMO 2017 THPT (Grades 10–12 shared) National Final (Heat) Set 04 Question 5

HKIMO · HKIMO 2017 THPT (Grades 10–12 shared) National Final (Heat) Set 04

Question 5

There are $15$ white, $16$ yellow and $12$ brown chopsticks mixed together. With eyes closed, how many must you take to guarantee one pair that is not white and another pair that is not yellow?

Editorial working convention: A pair consists of two sticks of the same colour; the two pairs must use four distinct sticks.