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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 \(00:00:00\).
Image Credit: http://www.prestonlibrary.net/blog/wp-content/uploads/2009/04/clock.gif

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