Note that all 6 digit numbers work, so there are \(6 \times 6 \times 6 \times 6 \times 6 \times 6 = 46,656 \)numbers
Now, for the 5 digit numbers, there are \(6^5 = 7776\) numbers, but we need to count for the numbers that are less than 23,000.
If the first digit is a 1, there are \(6^4 = 1296\) numbers that don't work
If the first two digits are 21, there are \(6^3 = 216\) numbers that don't work
LIkewise, if the first two digits are 22, there are 216 numbers that don't work
So, there are \(46,656 + 7776 - 1296 - 216 - 216 = \color{brown}\boxed{52704}\)
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