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Problems
Contests
National and Regional Contests
China Contests
XES Mathematics Olympiad
the 16th XMO
4
4
Part of
the 16th XMO
Problems
(1)
Springs are fired inXMO
Source: 16thXMO
6/22/2024
Given an integer
n
n
n
,For a sequence of
X
X
X
with the number of
n
n
n
and
Y
Y
Y
with the number of
100
n
100n
100
n
, we call it a spring . We have two following rules
■
\blacksquare
■
Choose four adjacent character , if it is
Y
X
X
Y
YXXY
Y
XX
Y
, than it can be changed into
X
Y
Y
X
XYYX
X
YY
X
■
\blacksquare
■
Choose. four adjacent character , if it is
X
Y
Y
X
XYYX
X
YY
X
, than it can be changed into
Y
X
X
Y
YXXY
Y
XX
Y
If spring
A
A
A
can become
B
B
B
using the rules , than we call they are [color=#3D85C6]similar Thy to find the maximum of
C
C
C
such that there exists
C
C
C
distinct springs and they are [color=#3D85C6]similar
contests
combinatorics