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Baltic Way 2023 counting and probability
Problem
A robot moves along the lines of an infinitely large square grid. It starts at an intersection and turns at each intersection it encounters. At some point it reaches its starting point without having visited any other point twice. What are the possible path lengths of the robot?
Solution
Solution: See Solution of C2.
Final answer
Exactly the integers divisible by four other than eight; that is, 4 and all integers at least 12 that are multiples of 4.
Techniques
Invariants / monovariantsColoring schemes, extremal arguments