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Mon 4 Jul, 2005 08:08 pm
There are many triangles on a plane. Each is divided into four parts by twomutually perpendicular diameters. Each part is painted either red, yellow or blue. No matter how the circles are rotated in a plane, they are
different from one another. At most how many circles are painted with all
three colours?
I have no idea where to begin.
Are they triangles or circles?
It sounds like the question is "How many ways are there to color the four quadrants of a circle with three colors independent of orientation?"
Since all three colors are to be used, each circle must have one color in two quadrants. Let's count the number of ways with red occupying two quadrants.
If the two reds are side-by-side, there are two different ways to assign the yellow and blue. If the two reds are opposite each other, there is only one way. Therefore, there are three ways with two reds.
Likewise, there are three ways each with two yellows and with two blues. Therefore, there are nine ways total.
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