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UKMT Intermediate Mathematical Challenge, 2025

Combinatorics Difficulty 3.0 AMC 10/12 Find the answer United Kingdom

Rob, Rog and Roy all painted some fence posts one day. Rob painted 45, Rog painted 51 and Roy painted 48. One of them painted twice as many posts in the morning as he did in the afternoon, a second one painted three times as many in the morning as in the afternoon and the third one painted four times as many in the morning as in the afternoon. Who painted the most fence posts in the morning?

(A) Rob (B) Rog (C) Roy (D) Rob and Roy, who painted the same number (E) Rob, Rog and Roy, who all painted the same number

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