Question 22. A triangular pyramid is built with 20 cannonballs as shown. Each cannonball is labeled with one of the letters A, B, C, D, or E. There are four cannonballs with each type of label. The picture shows the labels of the cannonballs on three of the faces of the pyramid. What is the label of the hidden cannonball in the middle of the fourth face? Now if we look at a pyramid and we laid it out flat, it would look like so. Now let's take a look at our three faces that we know. We take the first one and just move it over to the bottom to start matching our net. Then we can start making a flat net of a pyramid. We notice that this side has the balls D, A, D, A, which matches with the balls over here, D, A, D, A. So this can actually be rotated over and moved here and be adjacent in this way. Also notice D, B, E, C, which matches the D, B, E, C over here. So we can move this triangle over here. Now when this shape is folded up, some of the balls will repeat. So it will look something like this. The B, A, D will flip and then the C, E, D will flip on this side. And then we are left with the one unknown cannonball we're trying to find out. When this is connected into a pyramid, we will be missing a couple of the cannonballs since they overlap with each other. We can cross these out and then we can count up the total number of each type of ball. When we count them out, we get 4 of A, 4 of B, 4 of C, 3 of D, and 4 of E. So we know that the one ball that we don't see is D.

cannonball

triangular pyramid

labels

hidden

puzzle