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MathNet 2006 — Part 02 Question 37

Math Olympiad Vault · MathNet 2006 — Part 02

Question 37

There are 390 gold coins spread across 30 chests: 13 coins in each chest. Each coin weighs a whole number of grams, greater than or equal to 1 and less than or equal to 13, and there are 13 coins of each weight.
It is known that if two coins are in the same chest, the difference between their weights is less than or equal to 4 grams. Determine what is the minimum possible value of the weight of the contents of the heaviest chest.