Maths Olympiad Prep

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, 2026

Combinatorics Difficulty 5.0 AIME, harder Prove it United Kingdom

Starting at (0,0)(0,0), a frog makes 9999 jumps of distance 5\sqrt{5} between points on the lines y=1y=-1, y=0y=0 and y=1y=1, increasing its xx-coordinate by 11 or 22 each time. How many possibilities are there for the frog's final position?

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