x^3 + y^3 + z^3 = w^3
The smallest set of positive integers x,y,z,w qualifying as a solution of the bolded equation above is:
a.Find some other sets of distinct integers, not necessarily positive.
b. Provide some comments on "The sum of 3 cubes is a cube" equation.
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.