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Problems
Contests
National and Regional Contests
Korea Contests
Korea National Olympiad
2006 Korea National Olympiad
8
8
Part of
2006 Korea National Olympiad
Problems
(1)
27 students
Source: 2006 Korea National Olympiad #8
3/18/2018
27
27
27
students are given a number from
1
1
1
to
27.
27.
27.
How many ways are there to divide
27
27
27
students into
9
9
9
groups of
3
3
3
with the following condition?(i) The sum of students number in each group is
1
(
m
o
d
3
)
1\pmod{3}
1
(
mod
3
)
(ii) There are no such two students where their numbering differs by
3.
3.
3.
combinatorics
counting