Puzzle 30: Darkness

Let there be light:

Darkness has descended on the plane of Mopok. All electricity has been cut-off by the Trydan Corporation. All they have to light the plane are k lighthouses that run on cooking oil where k ≥ 1 is a positive integer. They can be kept going indefinitely, the Mopoks love their french fries, but each lighthouse can only illuminate a sector of 360/k degrees. The lamp of each lighthouse can be rotated but it must be fixed before the light is turned on. Can the lights be rotated so that the whole plane is covered?
(The lighthouses positions are given, you don’t get to choose where to put them)
(Assuming that k is even makes the problem a bit easier).





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