Removing digits

Number Theory Level 5

Find the number of integers \(N\) between \(1\) and \(1000000000=10^9\) (inclusive) such that crossing out the first digit of \(N\) results in the integer \(\frac{N}{25}\)?

Details and assumptions

As an explicit example, crossing out the first digit of the integer \(102\) results in the integer \( 2\).

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