We own a regular 12-hour digital clock that displays its output on the ceiling at night (a nice feature when your vision isn't what it once was). The only problem is that there's no colon or space dividing the hours and minutes, so depending on where I am in the room when I look up at the ceiling, I may be reading the display upside-down. For instance, the clock may read "122" if I'm looking at it right-side up, but "221" if I'm reading it upside-down.

At certain times each day, however, the clock reads the same whether it's read right-side up or upside-down, like:

So, given this example image and the information above:

How many times in a 24-hour day
would the clock appear to read the same
both upside-down and right-side-up?

Here is the SOLUTION.

THE SOLUTION:

There are 54 times during the day when this will occur; at the following 27 instances (both AM and PM):