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#1 2015-09-28 23:34:26

Yoran
Guest

Clock in the mirror - Alternative Solution

In case not discussed before, I have the following alternative Solution to the Clock-in-the-mirror puzzle:

Solution:
- The mirror inverts the clock 180 deg around the 12-6 hrs  vertical Axis.
- Let Tm and Td denote the mirror and departure times, respectively,
   Then the effect of the inversion is such that:
         
         Tm+Td = 12  for all times around the vertical axis 
   Or   Td = 12 -Tm  ........................(1)
- Let Ta denote the arrival time
- Given:
         
         Td+20/60 =Ta ......................(2)
     
         Tm=Ta-2.5  ..........................(3)

Now, substituting (3) into (1) and substituting for Td in (2), we get

      Tc =12-Tc+2.5+20/60
=> Tc = 7.416666666667 hours
          = 7hrs + (0.41666667*60min)
          = 7:25

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