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.

Hours that can be vertically flipped:-

I, II, III, IX, X, XI, XII, XIII, IXX, XX, XXI, XXII, XXIII, -

Minutes that can be vertically flipped:-

I, II, III, IX, X, XI, XII, XIII, IXX, XX, XXI, XXII, XXIII, IXXX, XXX, XXXI, XXXII, XXXIII, -

For a 12 hour clock, only the first 7 hours apply, but all 14 apply for a 24 hour. All 19 minute setups work for both the 12 and 24 hour formats.

For a 12 hour clock, 7*19 = 133 minutes out of 720 (12 hours) can be reflected.

For a 24 hour clock, 14*19 = 266 minutes out of 1440 can be reflected, which is the same proportion as the 12 hour clock, assuming that the 24h clock shows -:-- at midnight.

By the way, where did you get your clock? Do they have to be made to order? I want one.

Posted by Iain on 2004-05-17 07:41:49