MathDB
Problems
Contests
National and Regional Contests
Indonesia Contests
Indonesia MO
2016 Indonesia MO
8
8
Part of
2016 Indonesia MO
Problems
(1)
Indonesian MO 2016 Last Problem
Source: Indonesian MO 2016 Problem #8
5/2/2017
Determine with proof, the number of permutations
a
1
,
a
2
,
a
3
,
.
.
.
,
a
2016
a_1,a_2,a_3,...,a_{2016}
a
1
,
a
2
,
a
3
,
...
,
a
2016
of
1
,
2
,
3
,
.
.
.
,
2016
1,2,3,...,2016
1
,
2
,
3
,
...
,
2016
such that the value of
∣
a
i
−
i
∣
|a_i-i|
∣
a
i
−
i
∣
is fixed for all
i
=
1
,
2
,
3
,
.
.
.
,
2016
i=1,2,3,...,2016
i
=
1
,
2
,
3
,
...
,
2016
, and its value is an integer multiple of
3
3
3
.
permutations
combinatorics
number theory