Buying House Numbers

In a new housing project, the owners need to buy new house numbers from the only hardware store in their area. The houses are numbered \( 1, 2, 3, 4, 5, \ldots\), and the owners purchase the digits for their house numbers in numerical order ( i.e. \(1, 2, 3, \ldots\)). If the store has exactly \(100\) of each digit, what is the address of the first home owner who is unable to purchase their house number?

Details and assumptions

The store has exactly 100 of each digit \( 0, 1, 2, 3, 4, 5, 6, 7, 8, 9\). \(10\) is not considered a digit.

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