Digital Clock Times Puzzle

The Puzzle:

Digital Clock Times

Tim saw that his oven digital clock was showing 1:23, and noticed that each number was one higher than the number to its left.

He wondered: of all the different clock times from 0:00 to 12:59, how many are like that? And what exactly are those clock times?

Can you help Tim out?

Do you have the answer? Check against our solution!