Combinatorics · Parity · Lattice walks · Invariants
Problem 1, 2007
A car leaves town \(A\) and drives along a straight road at constant speed. Every \(15\) minutes it makes a turn of \(90\) degrees, to the left or to the right. Prove that the car can be back in \(A\) only after a whole number of hours.
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Serbian Municipal Competition 2007, high school grade I, category A, problem 1. Organized by the Mathematical Society of Serbia (DMS). Source