Six nervous young recruits stand in a single line for their first drill session. They face the gruff drill sergeant, who barks out their first order—"Left Face"—and in one second they do this: Oops! Not all of them got it right. But what now? All of the recruits are nervous. When two soldiers see that they are face to face, they both assume they are wrong and (in exactly one second!) turn the other way. After one second, the soldiers look like this: Each second, they react the same way. The sergeant rolls his eyes and decides to wait for them to settle down before giving another order. How long will it take before that next order can be given? What if a different recruit—say one at the end of the line—turns right instead of left? How long could it take? What initial setups take the longest to settle down? What if more than one recruit turns the wrong way? Is it possible to predict the final configuration just by looking at the starting position? What if there are 10 recruits? Or just 3? How would your answers to the previous questions change, depending on the number of recruits? Making Mathematics Home | Mathematics Projects | Students | Teachers | Mentors | Parents | Hard Math Café | Raw Recruits Project Description | Prerequisites | Warm Up Problems | Hints | Resources | Teaching Notes | Extensions | Results |
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