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?
Well, If he has 4 kinds of flowers, then he has 4 choices for the first quadrant, 3 choices for the second quadrant, 2 choices for the third quadrant and finally 1 choice for the fourth quadrant(this is based on his desire not to have adjacent quadrants planted with same kind of flower.)
So: 4 x 3 x 2 x 1 = 24 different gardens of flowers that he could plant.
Note: I didn't understand what you meant by "the gardner can use the same flower more than once" Did you mean within a particular quadrant, or throughout the four quadrants?