# PnC in Geometry – 3-D painting 1

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

1. I think for the cuboid the ways of painting should be 360

2. Manoj |

Hi Sir,

While finding the number of ways to paint a cube, why didnâ€™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

• Ronnie |

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

3. Equilateral Triangle |

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.

• Shivani |

why is 5 multiplied?