math challenge

Weeks of November 2 - 15, 1997

Switch Which Way

Egor's hotel room has three light switches. Switches A, B, and C can all be flipped up or down. Currently, all three switches are flipped down and all the lights in the room are off. Each switch belongs to one specific light in the room, but Egor soon discovers that some cut-rate electrician has crossed the wires.

If Egor flicks switch A up, light B turns on.
If he flicks switch A down, light C turns off.
If he flicks switch B up, light C turns on.
If he flicks switch B down, light A turns off.
If he flicks switch C up, light A turns on.
If he flicks switch C down, light B turns off.

Egor flips the switches eight times in total. He doesn't flip any switch twice in a row, but does flip every switch at least two times. In the end, lights B and C remain on.

What sequence did Egor flip the switches to end up with these two lights on?
NOTE: There is more than one possible solution.


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