Test Cases for a clock

My company recently built an application, and it's currently in testing phase. One of it's feature if time validation.

It asks user to enter the time in HH:MM:SS format to set a alarm for that time. Note that the application only accepts the time as specified by the format HH:MM:SS,

where

SS,representing the second, should be in range[00,59]

MM,representing the minute, should be in range[0,59]

HH,representing the hour,should be in range[0,23]

Any other kind of data would be considered invalid by the application and it will print "Invalid".

For eg: 12:15:90 is an invalid time, 12/15/20 is also an invalid time format since application accepts hour, minute and second to be separated by colon ':' . 05:11:24 and 05:00:00 are valid as well.

My task is to test this application on several different test cases. The catch right now for me is all the test cases take unique different path. If two test cases take same path, they will be considered similar and will be counted as 1. For eg: 20:62:00 and 20:80:00, both will fall on the same restriction that Minute should be in the range [0,59]. Now the thing is I can only give in maximum of 100 test cases,and it needs to cover all the possible paths. I have thought of the main ones, but still think I am missing out on some. Can anyone help me out with kind of a list some good tricky ones.

P.S- The app can take string input as well as numeral input, as in a smartphone keyboard.