Problem number five. Julia cuts off the four vertices of a regular tetrahedron as shown. How many vertices does the shape that remains have? So let's zoom in on one of the vertices of the tetrahedron, and notice that if we imagine cutting off the dark gray vertex, we will form three new vertices circled in green, but we will actually lose one of the original vertices because that will get cut off. So that means that each cut we will lose one and gain three. So every cut we will get a net gain of two new vertices. And also notice that we initially had four vertices, and for each of our four cuts we will add two new vertices to our shape. So that means that the total number of vertices will be four, which is the initial, plus four times two. For each of the four cuts we get two vertices, and four plus four times two is equal to twelve. So that means that the answer is D, twelve.

geometry

tetrahedron

vertices

cutting

problem solving