2024 SSMO Accuracy Round Problems/Problem 1
Problem
Let a time of day be three-full if exactly three of its digits are 
s when displayed on a 
-hour clock in the 
format. How many seconds of the day are three-full?
Solution
Note that 
is a number from 
to 
and 
are both integers from 
to 
There are 
two-digit integers from to 
that have 
respectively. If contains a 
then there are 
possibilities. Otherwise, there are 
possibilities. Since the all times on the -hour clock appear twice each day, our answer is 
~SMO_Team
