Question
There are 5778 extinguished lamps arranged at equal distances on a circle. Below each lamp is a button. Pressing a button changes the state of 4 lamps: the lamp next to the button, the next two lamps in the circle clockwise, and the lamp opposite the button (an extinguished lamp lights up when its state is changed, and a lit lamp is extinguished). What is the maximum number of lamps that can be lit simultaneously?
Topics:
Combinatorics
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Combinatorial Geometry
Combinatorics
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Invariants
Logic
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Reasoning / Logic
Number Theory
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Division
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Parity (Even/Odd)
Combinatorics
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Case Analysis / Checking Cases
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Processes / Procedures
Combinatorics
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Colorings
- Beno Arbel Olympiad, 2017, Grade 8 Question 8
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