7 thoughts on “PnC in Geometry – 3-D painting 1

  1. Hi Sir,

    While finding the number of ways to paint a cube, why didn’t we consider a factor of 6 ways for selecting the first colour (red in the given example)?

    • We are assuming a cube freely floating in space (i.e. i can turn/twist it in any direction). So when unpainted, all the faces will be effectively identical. So since every colour has to appear once, I just arbitrarily chose a colour and a position for it and then decided where to place the other colours relative to it. You could have started with any colour, it would make no difference.

      regards
      J

      • But sir while fixing 1 side with a color , what is wrong with the following :-
        like first choosing a side from 6 identical sides= 1 way
        and then coloring it with any of the 6 colors =6c1 ways
        so shouldn’t it be 6c1*1 ?

      • Until you have painted one colour, the sides don’t become distinct. Everything will be measured wrt to the first painted side.

        regards
        J

  2. In the cube case,after painting first two opposite sides,the remaining four sides can be viewed as four places in a circle.So they can be arranged in 3! ways.So total no of ways is 5*3!=30 ways.

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