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239 Open Math Olympiad
2021 239 Open Mathematical Olympiad
6
6
Part of
2021 239 Open Mathematical Olympiad
Problems
(1)
Combinatorics about words
Source: 239 MO 2021 (10-11).6
5/2/2021
The alphabet of the tribe AAB consists of the only letters
A
A
A
and
B
B
B
. However, if you insert or delete the combination
A
A
A
AAA
AAA
or
B
B
B
BBB
BBB
for any words, the meaning of the word will not change. In addition, if
A
B
AB
A
B
is replaced with
B
B
A
A
BBAA
BB
AA
, or vice versa, the meaning of the word doesn't change. The same holds for
B
A
BA
B
A
and
A
A
B
B
AABB
AA
BB
. Is it true that
A
B
AB
A
B
and
B
A
BA
B
A
have the same meaning?
combinatorics