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Australian Intermediate Mathematics Olympiad 2022 Question 5

AIMO AUSTRALIA · Australian Intermediate Mathematics Olympiad 2022

Question 5

There are 5 lily pads on a pond, arranged in a circle. A frog can only jump from each lily pad to an adjacent lily pad on either side. How many ways are there for the frog to start on one of these lily pads, make 11 jumps, and end up where it started?

Numerical answer only; a non-negative integer less than 1000.