Wild About Math! Making Math fun and accessible

Couple of carnivals and a clever clock conundrum

Two Math carnivals have recently been published:

1. The 68th Carnival of Mathematics at +plus magazine
2. The 2nd Mathematics and Multimedia Blog Carnival at the Mathematics and Multimedia Blog.

Now, here's a challenging adaptation of a problem I recently discovered. I won't reveal the source till later to not give away the problem.

There's something interesting about the time 2:26 and other times of the day. This interesting thing can be seen over 100 times per day. What is the property and exactly how many times does it occur in a day?