As I look in the bathroom mirror while I'm shaving, I can see the reflection of the digital clockin my bedroom

Question

. Sometimes the time I see in the mirror( a reflection of the actual time) is the same as the actual time. How many times does this happen per day? (ignore the colon, because I can't see that anyway-the clock is to far away.)

Answer 1

4 times, 11:11 , 00:00, 10:01, 01 :10

Answer 2

It happens 22 times in a day. Here's how:

The only 4-digt times that have symmetry like this have to begin with a 1, because the hour number for all 2-digit hours must be 1. So in order to be symmetric, it must end in 1 too. I'm assuming of couse that your clock isn't in military time! Take each hour (10, 11, 12) and mirror it to give you: 10:01, 11:11, and 12:51.

If we ignore the colon entirely and look at 3-digit times (which are the only other types of times), the middle digit has to look the same itself in a mirror. The only digits that do this are 1, 8, and 0. But you can't have an 8 as the middle digit, because that would be the tens digit for the minutes, which can only go from 0 to 5. So the middle has to be 0 or 1. The end digits have to be reflections of each other. The only pairs of numbers that do this are 0 and 0, 1 and 1, 2 and 5, or 8 and 8. We can't have 0 because this has to be the hours digit too. So this leaves the following possibilities:

1:01, 1:11, 2:05, 5:02, 2:15, 5:12, 8:08, 8:18.

Combining this with the others, we see there are 11 different times total. So to answer the question of how many times it happens in a day, that would be 22.