MathDB

One day Mnemosyne decided to colour all natural numbers in increasing order. She coloured

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1

and

2

in brown, and her favourite number,

3

, in gold. From then on, for any number whose sum of digits (in the decimal system) was a golden number less than the number itself, she coloured it gold, but coloured the rest of the numbers brown. How many four-digit numbers were coloured gold by Mnemosyne? The set of natural numbers includes

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Problem Statement