hard · GMAT Quant

An autonomous mobile robot executes a sequence of 5 movement commands (n = 1, 2, 3, 4, 5). Each command is selected from four options: Forward (F), Turn (T), Reverse (R), or Stop (S). Stop (S) is a safety state that is never activated during navigation. The command sequence must follow three rules: at n = 1 the robot must execute command F, command R cannot occur on two consecutive steps, and command T and command R cannot directly follow one another in either order (T to R and R to T are both forbidden).

How many valid 5-step movement sequences end in command R at n = 5?

  1. 3
  2. 6
  3. 9
  4. 12
  5. 16

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