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A gardener has a circular garden, which he divides into four quadrants. He has four different kinds of flowers, and he wants to assign a flower to each quadrant, so that adjacent quadrants are not planted with the same kind of flower. (Also, the gardener can use the same flower more than once.) How many different gardens are possible?
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 May 1, 2019
 #1
avatar+5232 
+2

My bad, let's start again

 

A can take four flowers,  B can take 3

 

Then there are 3 choices for C.

 

If C=A there are 3 choices for D

if C!=A there are 2 choices for D

 

So we have

 

4 x 3 x (3 + 2x2) = 4 x 3 x 7 = 84

 May 1, 2019
edited by Rom  May 2, 2019
 #2
avatar+70 
+1

Why are there 3 choices for C?

Bxtterman  May 1, 2019
 #3
avatar+5232 
+1

C just has to not have a flower in common w/B (and D, but we enforce that on D not C)

Rom  May 1, 2019
 #4
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0

The answer is wrong.

 May 1, 2019
 #5
avatar+5232 
+1

see edited version

Rom  May 2, 2019
edited by Rom  May 2, 2019

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