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Number theory Difficulty 3.0 AMC 10/12 Prove it United Kingdom

There are 2021 balls in a crate. The balls are numbered from 1 to 2021. Erica works out the digit sum for each ball. For example, the digit sum of 2021 is 5, since $2 + 0 + 2 + 1 = 5$ . Erica notes that balls with equal digit sums have the same colour and balls with different digit sums have different colours. How many different colours of balls are there in the crate?

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