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Esteban the alchemist

Source: 2022 Centroamerican and Caribbean Mathematical Olympiad, P5

December 1, 2022
combinatoricsmagic

Problem Statement

Esteban the alchemist have 80888088 copper pieces, 60666066 bronze pieces, 40444044 silver pieces and 20222022 gold pieces. He can take two pieces of different metals and use a magic hammer to turn them into two pieces of different metals that he take and different each other. Find the largest number of gold pieces that Esteban can obtain after using the magic hammer a finite number of times.
<spanclass=′latex−bold′>Note:</span><span class='latex-bold'>Note:</span> If Esteban takes a copper and bronze pieces, then he turn them into a silver and a gold pieces.
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