Div divis divisible

Number Theory Level 5

Determine how many \(1000\) digit numbers \(A\) have the following property:

When any digit of \(A\), aside from the first, is deleted to form a \(999\) digit number \(B\), then \(B\) divides \(A\).

Details and assumptions

As an explicit example, the number 1000 is a 4-digit number that satisfies the above property.

The number \(12=012\) is a 2-digit number, not a 3-digit number.


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