Okay, now I think I got Republican's rope riddle. This is how I'd do: Say Rope A and B. 1. Double the rope A by joining the two opposite ends. 2. Quadruple the rope B by joining the two opposite ends, and repeating it. 3. Burn the rope A. After it completely burns up, 30 minutes has elapsed. 4. As soon as A finishes burning, burn the rope B. After it finishes burning, which takes 15 minutes, the total time will be 30 + 15 = 45 minutes. :)