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4

Part of 2010 Federal Competition For Advanced Students, P2

Problems(1)

ways are there to move from (0, 0) to (n, 2), under lattice point conditions

Source: 41st Austrian Mathematical Olympiad National Competition (Final Round, part 2) 3rd June 2010 p4

9/5/2019
Consider the part of a lattice given by the corners (0,0),(n,0),(n,2)(0, 0), (n, 0), (n, 2) and (0,2)(0, 2). From a lattice point (a,b)(a, b) one can move to (a+1,b)(a + 1, b) or to (a+1,b+1)(a + 1, b + 1) or to (a,bāˆ’1(a, b - 1), provided that the second point is also contained in the part of the lattice. How many ways are there to move from (0,0)(0, 0) to (n,2)(n, 2) considering these rules?
combinatoricscombinatorial geometrylattice points