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Extremely tricky maths problem on 11+ paper

Carla wants to paint the 4 walls of her bedroom. She has 5 different colours. She may use a colour on more than one wall, but she does not want the same colour on adjacent walls. In how many different ways could Carla paint her bedroom?

Can someone please solve this?
Reply 1
Original post by ishanth
Carla wants to paint the 4 walls of her bedroom. She has 5 different colours. She may use a colour on more than one wall, but she does not want the same colour on adjacent walls. In how many different ways could Carla paint her bedroom?

Can someone please solve this?

this is from quora:

A color for A can be chosen 5 ways.
[start]The color for B can be any of the 5 except that of A and hence can be chosen in 4 ways.[/start]
[start]The color for C can be any one except that of B and also can be chosen in 4 ways.[/start]
[start]Lastly , the color for D is any except that of C and again can be chosen in 4 ways.[/start]
[start]So the 4 rectangles can be colored in 5.4.4.4 = 320 ways.[/start]

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