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Problems
Contests
International Contests
Tournament Of Towns
1988 Tournament Of Towns
(190) 3
TOT 190 1988 Autumn J3 S=sum a_k /k
TOT 190 1988 Autumn J3 S=sum a_k /k
Source:
March 6, 2021
number theory
permutations
Problem Statement
Let
a
1
,
a
2
,
.
.
.
,
a
n
a_1 , a_2 ,... , a_n
a
1
,
a
2
,
...
,
a
n
be an arrangement of the integers
1
,
2
,
.
.
.
,
n
1,2,..., n
1
,
2
,
...
,
n
. Let
S
=
a
1
1
+
a
2
2
+
a
3
3
+
.
.
.
+
a
n
1
.
S=\frac{a_1}{1}+\frac{a_2}{2}+\frac{a_3}{3}+...+\frac{a_n}{1}.
S
=
1
a
1
+
2
a
2
+
3
a
3
+
...
+
1
a
n
.
Find a natural number
n
n
n
such that among the values of
S
S
S
for all arrangements
a
1
,
a
2
,
.
.
.
,
a
n
a_1 , a_2 ,... , a_n
a
1
,
a
2
,
...
,
a
n
, all the integers from
n
n
n
to
n
+
100
n + 100
n
+
100
appear .
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