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First (left-most) digit can be any from 1 to 9.
Next (tens) digit can be any from 0 to 9.
Therefore, there are 9*10 = 90 such three-digit numbers.
Solved.
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Even more simple reasoning is possible.
Consider the set of all such 3-digit numbers.
Cut the last digit: you will get the set of all 2-digit numbers.
The cardinality of this set of 2-digit numbers is 90 - - - it gives the answer.