Problem number 16. Nora is playing with three cups on the kitchen table. In each move, she takes the cup on the left, flips it over, and puts it to the right of the other cups. The picture shows the first move. What do the cups look like after 10 moves? A, B, C, D, or E? I'm going to redraw the cups down here just to make it a little easier to see. One, two, three cups. The picture shows the first move. The first move involves taking the cup on the far left and flipping it upside down and moving it on this side. That's move one. And in fact, in the first three moves, each of these cups will end up upside down. So move two will be here and move three will be here. Now the three cups at this point are these three, and they're no longer here. As we can see, three moves flip all the cups. So in the next three moves, those would be moves four through six, the three cups then become right side up again. In moves seven through nine, the next three moves, they are now upside down. The problem asks us what this looks like after 10 moves. Well, in the 10th move, Nora will take this cup on the far left, which was upside down, and she will flip it so it's right side up. So what she's left with after 10 moves are two cups that are upside down and one that's right side up. And this is answer B.

cup game

flipping cups

upside down

right side up

configuration