2020 CIME I Problems/Problem 1
A knight begins on the point in the coordinate plane. From any point the knight moves to either or . Find the number of ways the knight can reach the point .
Let denote a move of units north and unit east, and let denote a move of unit north and units east. To get to the point using only these moves, say moves in direction and moves in direction , we must have because both the - and -coordinates have increased by since the knight started. Solving this system of equations gives us . This means we need the knight to make moves, of which are headed in direction , and the remaining are headed in direction . Any combination of these moves work, so the answer is
https://www.youtube.com/watch?v=SFVt0JYLkHY ~Shreyas S
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