3. Questions 6-12

A square parking lot has exactly eight lights-numbered 1 through 8-situated along its perimeter as diagramed below:

North
1------------2------------３
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　 West 8　4 East
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7------------6------------5
South

The lot must always be illuminated in such a way that the following specifications are met:
At least one of any three consecutively numbered lights is off.

Light 8 is on.
Neither light 2 nor light 7 is on when light 1 is on.
At least one of the three lights on each side is on.
If any side has exactly one of its three lights on, then that light is its center light.
Two of the lights on the north side are on.

(6). Which one of the following could be a complete and accurate list of lights that are on together?
(A) 1,3,5,7
(B) 2,4,6,8
(C) 2,3,5,6,8
(D) 3,4,6,7,8
(E) 1,2,4,5,8

(7). Which one of the following lights must be on?
(A) light 2
(B) light 3
(C) light 4
(D) light 5
(E) light 6

(8). If light 1 is off, which one of the following is a light that must also be off?
(A) light 3
(B) light 4
(C) light 5
(D) light 6
(E) light 7

(9). Which one of the following statements must be true?
(A) If light 2 is on, then light 6 is off.
(B) If light 3 is on, then light 2 is on.
(C) If light 4 is on, then light 3 is off.
(D) If light 5 is off, then light 4 is on.
(E) If light 6 is off, then light 1 is on.

(10). If light 5 is on, which one of the following could be true?
(A) light 1 is off and light 6 is off.
(B) light 1 is on and light 7 is on.
(C) light 2 is off and light 4 is on.
(D) light 2 is off and light 6 is off.
(E) light 6 is on and light 7 is on.

(11). If light 4 is on, each of the following statements must be true EXCEPT:
(A) Light 1 is on.
(B) Light 2 is on.
(C) Light 5 is off.
(D) Light 6 is on.
(E) Light 7 is off.

(12). Suppose that it is no longer part of the specifications that two lights on the north side be on. If all of the other original specifications remain the same, and if exactly one light on the north side is on, which one of the following statements could be false?
(A) Light 1 is off.
(B) Light 2 is on.
(C) Light 3 is off.
(D) Light 4 is on.
(E) Light 5 is on.

KEYS: CBBDABE