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Since we can cut the rope with the help of a pair of scissors, the rope can be cut in half, which is equivalent to having two ropes of 30 minutes long. Lay them in rows and set fire to opposite ends. The flames will meet at the center and we will have a 15 minutes rope. Set the fire to the other end of the smaller rope, so that it burns down to 7.5 minutes. Then set fire to the other end of the remaining rope, which will finish burning in 3.75minutes.

Therefore the smallest time interval that can be measured is 3.75 minutes.

They are Triplets.