The field of a new soccer stadium is watered by three individual sprinkler systems, as shown by the A, B, and C regions in the figure below. Each sprinkler system is controlled by exactly one of three on-off valves in an underground maintenance room, and each sprinkler system can be turned on without turning on the other two systems. Each of the valves is presently in the off position, and the field is dry. The valves have not been labeled, so you do not know which valve controls which sprinkler system. You want to correctly label the valves as A, B, and C. You also want to do it by making only one trip up to the field. You cannot see the field from the maintenance room, and no one is available to help you. What procedure can you use to determine how to correctly label the valves? Assume that all of the valves and all of the sprinkler systems are operating properly. Also assume that the sprinklers are either completely off or completely on. Explain your reasoning.
The field of a new soccer stadium is watered by three individual sprinkler systems, as shown by the A, B, and C regions in the figure below. Each sprinkler system is controlled by exactly one of three on-off valves in an underground maintenance room, and each sprinkler system can be turned on without turning on the other two systems. Each of the valves is presently in the off position, and the field is dry. The valves have not been labeled, so you do not know which valve controls which sprinkler system. You want to correctly label the valves as A, B, and C. You also want to do it by making only one trip up to the field. You cannot see the field from the maintenance room, and no one is available to help you. What procedure can you use to determine how to correctly label the valves? Assume that all of the valves and all of the sprinkler systems are operating properly. Also assume that the sprinklers are either completely off or completely on. Explain your reasoning.
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