Michael's huge numbers

Number Theory Level 4

Call a number huge if the sum of its digits is greater than or equal to \(23.\) There are \(35\) huge three-digit numbers, and there are \(2205\) huge four-digit numbers. If \(N\) is the number of huge five-digit numbers, what are the last three digits of \(N\)?

This problem is posed by Michael T.

Details and assumptions

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


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