# 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.