Question number 17. Each of the segments in the figure needs to be colored one of three colors, red, green, or blue. Each of the four triangles needs to have one side of each of the different colors. Three of the segments have already been colored as indicated. What color and the segment marked with X be? And here's our figure. I will make a copy of it, and I will enlarge this image so we can see what is going on. And let me also use some color over here since I'm allowed to do that. I'll color code the edges. So the blue edge, let's actually use blue here to denote that. And then we'll have red for the two edges marked in red. Okay, so we're focused on the edge denoted by X. And we have here two triangles already containing a red edge, so these are the ones where I placed the red dot. In these triangles, we may not use red again. So in particular, this edge that I'm outlining, that cannot be red. And this edge that I'm outlining, that cannot be red. So the possibilities for those edges are, well, we could use blue over here if we really want it. And we could use blue over here if we really want it, but not at the same time. So we could also use green over here, and we could use green over here, but not at the same time. So those are the two possibilities for the sides of this triangle containing X. One of them will be green, the other one will be blue. What color can be applied to the edge with X on top of it? Well, if each triangle has a side of each of the three colors, then the only remaining color here is red. And so we have determined that only red can be applied to this edge, and the answer to the problem is C, only red.

coloring problem

triangles

color elimination

red segment

video explanation