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2020 Princeton University Math Competition
8
8
Part of
2020 Princeton University Math Competition
Problems
(1)
2020 PUMaC Team 8
Source:
1/1/2022
Let there be a tiger, William, at the origin. William leaps
1
1
1
unit in a random direction, then leaps
2
2
2
units in a random direction, and so forth until he leaps
15
15
15
units in a random direction to celebrate PUMaC’s 15th year. There exists a circle centered at the origin such that the probability that William is contained in the circle (assume William is a point) is exactly
1
/
2
1/2
1/2
after the
15
15
15
leaps. The area of that circle can be written as
A
π
A\pi
A
π
. What is
A
A
A
?
combinatorics