Each of five lights in a circle have been assigned to a switch: The switch for l

Question

Each of five lights in a circle have been assigned to a switch: The switch for light A changes the state (on or off) of lights A, c, D. The switch for light B changes the state (on or off) of lights A, B,C The switch for light C changes the state (on or off) of lights B,C, D. The switch for light D changes the state (on or off) of lights C, D.E The switch for light E changes the state (on or off) of lights B, C, E. There are 32 possible combinations for these lights to be on or off. Given these funny switches, is it possible to produce all 32 combinations if all of the lights are off to start with?

Explanation / Answer

Let the switches be numberedin the order 1 2 3 4 5

No, it is not possible to make all the 32 combinations.
Eventhough many combinations can be made like:-
Switch 1 -ACD
Switch 1&2 - BD
Switch 1,2&3 - C
etc.
But the combination where all bulbs A,B,C,D & E are on can never be made using any combination because any one switch will switch off a bulb which was switched on by some previous bulb.
Therefore since ABCDE can not be switched on at the same time thus all 32 combinations are not possible.

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