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Montgomery Blair
MBMT Guts Rounds
2015.21
2015.21
Part of
MBMT Guts Rounds
Problems
(1)
MBMT Guts #21
Source:
3/29/2015
A bug starts at vertex
A
A
A
of triangle
A
B
C
ABC
A
BC
. Six times, the bug travels to a randomly chosen adjacent vertex. For example, the bug could go from
A
A
A
, to
B
B
B
, to
C
C
C
, back to
B
B
B
, and back to
C
C
C
. What is the probability that the bug ends up at
A
A
A
after its six moves?