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10
2023 Combinatorics #10
2023 Combinatorics #10
Source:
February 28, 2024
combinatorics
Problem Statement
Let
x
0
=
x
101
=
0
x_0 = x_{101} = 0
x
0
=
x
101
=
0
. The numbers
x
1
,
x
2
,
.
.
.
,
x
100
x_1, x_2,...,x_{100}
x
1
,
x
2
,
...
,
x
100
are chosen at random from the interval
[
0
,
1
]
[0, 1]
[
0
,
1
]
uniformly and independently. Compute the probability that
2
x
i
≥
x
i
−
1
+
x
i
+
1
2x_i \ge x_{i-1} + x_{i+1}
2
x
i
≥
x
i
−
1
+
x
i
+
1
for all
i
=
1
,
2
,
.
.
.
,
100.
i = 1, 2,..., 100.
i
=
1
,
2
,
...
,
100.
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