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2019 CHMMC (Fall)
3
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Part of
2019 CHMMC (Fall)
Problems
(1)
2019 Fall Team #3
Source:
4/17/2022
A frog is jumping between lattice points on the coordinate plane in the following way: On each jump, the frog randomly goes to one of the
8
8
8
closest lattice points to it, such that the frog never goes in the same direction on consecutive jumps. If the frog starts at
(
20
,
19
)
(20, 19)
(
20
,
19
)
and jumps to
(
20
,
20
)
(20, 20)
(
20
,
20
)
, then what is the expected value of the frog’s position after it jumps for an infinitely long time?
combinatorics