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Putnam
2020 Putnam
A4
A4
Part of
2020 Putnam
Problems
(1)
Putnam 2020 A4
Source: 81st William Lowell Putnam Competition
2/22/2021
Consider a horizontal strip of
N
+
2
N+2
N
+
2
squares in which the first and the last square are black and the remaining
N
N
N
squares are all white. Choose a white square uniformly at random, choose one of its two neighbors with equal probability, and color tis neighboring square black if it is not already black. Repeat this process until all the remaining white squares have only black neighbors. Let
w
(
N
)
w(N)
w
(
N
)
be the expected number of white squares remaining. Find
lim
N
→
∞
w
(
N
)
N
.
\lim_{N\to\infty}\frac{w(N)}{N}.
N
→
∞
lim
N
w
(
N
)
.
Putnam
Putnam 2020