Problem number 19. Therese the tiler is planning to make a large square mosaic floor with a repeating pattern. She is using hexagonal and triangular tiles arranged as shown in the diagram. She thinks she will use 3000 hexagonal tiles to make the whole floor. Approximately how many triangular tiles will she need? In this problem, we can think about counting the number of triangles based on the number of hexagons. For example, we notice that each hexagon is next to six triangles. So the question is, is the answer just 3000, which is the number of hexagons times six, because each hexagon is next to six triangles? Well, the answer is actually no, because we notice that each triangle is actually counted three times. For example, the yellow triangle is countered by the red hexagon, the green hexagon, and the cyan hexagon. And so that means that we're counting each triangle three times. And so we need to divide our answer by three because we're over counting. And so that means the actual number of triangles is 3000 times six, but we have to divide by three, 3000 times six is 18,000. And 18,000 divided by three is 6000. So the answer is D 6000.

mosaic

hexagonal tiles

triangular tiles

tile counting

mosaic floor