@geniusraccoon Hmmm I think its because the three gears need to be in a triangle to move, because the gears wont work one vs one on a line, you will be missing the first and the third if u use a line
@Bella Both are actually correct. I believe Professor Loh first found 27 (mod 4) to be 3, and then doubled this to get 6. Professor Loh is emphasizing the simplification step, which makes working with larger numbers easier. And if we simplify this further, 6 is 2 (mod 4). So your calculator is not wrong; 27 + 27 is 2 (mod 4). But noting Professor Loh's strategy will help you solve these types of problems more efficiently 🙂