Maths Olympiad Prep

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Combinatorics Difficulty 4.4 AIME Find the answer Slovenia

Miha has 4 boxes. One of the boxes contains only 20 cent coins, another contains only 10 cent coins, one contains only 2 cent coins and another contains only 1 cent coins. Miha can take the coins from 3 different boxes, taking 1 coin from one of the boxes, 2 coins from another and 3 coins from the third box. At most how many cents can Miha take from the boxes?

Pick one

Solution

Miha will get the greatest amount by taking three 20 cents coins, two 10 cents coins and one 2 cents coin. The total in this case equals 82 cents.

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