I own a very unique clock. It is digital, but it displays the time in Roman numerals. It does this in the same way as a normal digital clock (hours : minutes). The clock does not display seconds. For example, at 7:34 the clock displays "VII:XXXIV". Whenever a zero is required it is represented by a dash (-). That is, 1:00 is represented by "I:-".

Sometimes I place this clock on a flat, horizontal mirror which reflects what is displayed on the clock.

For what proportion of the day does the reflection of the time on the clock look the same as the time displayed by the clock itself?

Please provide an answer for both 12hr timing (the clock does not indicate the difference between AM and PM) and 24hr timing.

(In reply to My try by Iain)

I'm going to have to go ahead and disagree with you there... but only a little bit.

19 is not IXX (1 minus 20).  It's XIX (10 plus 10 minus 1).  Same goes for 29, it should be XXIX.

So that means that 39 is XXIX (and not IXL, which is maybe what you were thinking and why you left it out).

So that would give us 280/1440 for the 12 hour clock, and 280/1440 for the 24 hour clock with -:- for midnight, and 260/1440 for the 24 hour clock with 24:- for midnight.

Posted by nikki on 2004-06-03 18:54:22