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1985 IMO Longlists
13
IMO LongList 1985 CAN2 - Find the Average
IMO LongList 1985 CAN2 - Find the Average
Source:
September 10, 2010
LaTeX
number theory unsolved
number theory
Problem Statement
Find the average of the quantity
(
a
1
−
a
2
)
2
+
(
a
2
−
a
3
)
2
+
⋯
+
(
a
n
−
1
−
a
n
)
2
(a_1 - a_2)^2 + (a_2 - a_3)^2 +\cdots + (a_{n-1} -a_n)^2
(
a
1
−
a
2
)
2
+
(
a
2
−
a
3
)
2
+
⋯
+
(
a
n
−
1
−
a
n
)
2
taken over all permutations
(
a
1
,
a
2
,
…
,
a
n
)
(a_1, a_2, \dots , a_n)
(
a
1
,
a
2
,
…
,
a
n
)
of
(
1
,
2
,
…
,
n
)
.
(1, 2, \dots , n).
(
1
,
2
,
…
,
n
)
.
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