Discrete Mathematics Level 4

My digital 24-hour clock displays the time of day as three numbers $$X : Y : Z$$.

Let $$A$$ be the number of moments throughout a regular day (from midnight to midnight) when the digit sums of $$X,Y,Z$$ are all equal. Find $$\lceil 10^{-2} A \rceil$$.

Details & Assumptions:

• Ignore $$24:00:00$$ in favor of $$00:00:00$$.