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Omni-MATH / An ant starts out at (0,0). Each second, if it is currently at the square (x,y), it can move to (x−1,y−1),(x−1,y+1),(x+1,y−1), or (x+1,y+1). In how many ways can it end up at …

Problem

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problem

An ant starts out at (0,0)(0,0). Each second, if it is currently at the square (x,y)(x, y), it can move to (x−1,y−1),(x−1,y+1),(x+1,y−1)(x-1, y-1),(x-1, y+1),(x+1, y-1), or (x+1,y+1)(x+1, y+1). In how many ways can it end up at (2010,2010)(2010,2010) after 4020 seconds?
Plain-text mathematical notation (without MathML)
An ant starts out at (0,0). Each second, if it is currently at the square (x,y), it can move to (x−1,y−1),(x−1,y+1),(x+1,y−1), or (x+1,y+1). In how many ways can it end up at (2010,2010) after 4020 seconds?
Original LaTeX notation
An ant starts out at $(0,0)$. Each second, if it is currently at the square $(x, y)$, it can move to $(x-1, y-1),(x-1, y+1),(x+1, y-1)$, or $(x+1, y+1)$. In how many ways can it end up at $(2010,2010)$ after 4020 seconds?

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Source and history

task_id
878c2549-2669-50ff-acca-5e142e115099
task_key
test--878c2549-2669-50ff-acca-5e142e115099
task_revision_id
1
config / split
/ test

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