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Contests
National and Regional Contests
Vietnam Contests
Mathley Magazine
Mathley 2014-15
9
9
Part of
Mathley 2014-15
Problems
(1)
organizers want to rearrange 2014 students from same school in circle
Source: Mathley 2014.1 p9
8/20/2020
There are
2014
2014
2014
students from high schools nationwide communications sit around a round table in arbitrary manner. Then the organizers want to rearrange students from the same school sit next to each other by performing the following swapping: permutation view of two adjacent groups of students (see illustration). Find the smallest
k
k
k
number so that a result can be obtained results as desired by the organizers with no more than
k
k
k
swapping permits. Permission to change places like after
.
.
.
A
B
C
D
⏟
1
E
F
G
⏟
2
.
.
.
→
.
.
.
E
F
G
⏟
2
A
B
C
D
⏟
1
.
.
.
...\underbrace{ABCD}_\text{1}\underbrace{EFG}_\text{2}... \to ...\underbrace{EFG}_\text{2}\underbrace{ABCD}_\text{1}...
...
1
A
BC
D
2
EFG
...
→
...
2
EFG
1
A
BC
D
...
Vu The Khoi, Institute of Mathematics, Vietnam Academy of Science and Technology, Cau Giay, Hanoi.
combinatorics
geometry