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This question is asking what proportion of times can be flipped vertically and still remain the same.
The symbols that this clock uses are:
- = 0 = symetrical
I = 1 = symetrical
V = 5 = non-symetrical
X = 10 = symetrical
L = 50 = non-symetrical
An analysis of the minutes section shows that 19 of the 60 minutes are symetrical. Basically, any number that doesn't contain a V or an L.
This breakdown makes it more obvious:
0-9 - 5/10 symetrical
10-19 - 5/10 symetrical
20-29 - 5/10 symetrical
30-39 - 4/10 symetrical
40-49 - 0/10 symetrical
50-59 - 0/10 symetrical
As for the hours section, in 12hr mode the clock displays the numbers 1 through 12, with 7 of these 12 being symetrical. In 24hr mode the clock displays the numbers 0 through 23, with 14 of the 24 being symetrical (note that unlike 12hr mode, the clock displays "-" for 0, which is symetrical, instead of "XXIV" for 24, which isn't).
In order for a time to be symetrical, both the hour and minute section need to be symetrical. Therefore the proportion of symetrical times is simply the product of the proportion of symetrical hours and proportion of symetrical minutes.
For 12hr mode:
(19/60) * (7/12) = (133/720)
= 18.47% (2d.p.)
For 24hr mode:
(19/60) * (14/24) = (266/1440)
= 18.47% (2d.p.)
P.S. I don't really own this clock, but I wish I did. It would be really confusing to read, but it would make a great conversation piece! |
