The distance between points A and B is 18 centimeters, how many points M are on the beam AB, such that / BM / = 20cm.

Since the distance from the beginning of the beam AB of point A to point B is 18 centimeters, then there is only one point M on the beam that satisfies the condition / BM / = 20 cm and this point is on the other side of point B relative to point A. There is still one point M1, located at a distance of 20 cm from B, but it does not belong to the ray AB, and, therefore, does not satisfy the condition of the problem.
Answer: 1 point.