Grades 3-4 Video Solutions 2020-2020Levels34prob9

Video Transcription

Problem number nine. Cindy colors each region of the pattern red, blue, or yellow. She colors  regions that touch each other with different colors. She colors the outer ring or region of the pattern red. How many regions does Cindy color red? A, 1, B, 2, C, 3, D, 4, or  E, 5. The best way to solve a problem like this is to actually color in the regions. If you're doing this on the computer, you can draw the shape on a center piece of paper.  And if you don't have colored pencils, you can mark each region of the letter R for red, B for blue, and Y for yellow. I'm going to color in on the screen here, and we'll see  what we get as the answer. We know from the problem that Cindy colors the outer ring red. The next two regions, the one here and the one here, both touch the red region, so one  will have to be blue and the other yellow. Let's make the bottom one blue and the top one yellow. Next, we have a region here that touches both the yellow and the blue. You  can see on this side as well. So this one will have to be red. This region touches red and yellow, so it will need to be blue. In the same way, the region here needs to be  yellow, and the central region has to be red. Now there is another way that we can go about this. Again, we already know that the outer region is red. Let's make the inside  bottom region yellow and the one on top blue. We're swapping the colors. At this point, we see the same thing happening as before. The region here borders both yellow and blue,  so it has to be red. And this region will need to be yellow, this one blue, and this one red. So no matter which way we start with the blue and the yellow, we end up with exactly  the same regions colored red. And there are one, two, three of them. So the correct answer is C, three. Cindy colors three of the regions red.

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