Combinatorics · Hamiltonian paths · Grid boards · Recursion
A snake starts in the upper-left cell of a \(2 \times n\) board, where \(n\) is a natural number. From one cell it may move to another whenever the two cells share an edge, but it may never visit a cell twice. In how many ways can the snake visit every cell of the board?
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Serbian Municipal Competition 2020, high school grade I, category A, problem 2. Organized by the Mathematical Society of Serbia (DMS). Source