In the minimal-time solutions, the general sends to the right signals at speeds . The signal reflects at the right end of the line, and meets signal (for ) at cell . When reflects, it also creates a new general at the right end. Signals are constructed using auxiliary signals, which propagate to the left. Every second time a signal moves (to the right), it sends an auxiliary signal to the left. moves on its own at speed 1 while each of the slower signals moves only when it gets an auxiliary signal.