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All-Russian Olympiad Regional Round
1996 All-Russian Olympiad Regional Round
11.8
11.8
Part of
1996 All-Russian Olympiad Regional Round
Problems
(1)
infinite periodic sequence of 2 letters - All-Russian MO 1996 Regional (R4) 11.8
Source:
9/23/2024
Is there an infinite periodic sequence consisting of the letters
a
a
a
and
b
b
b
, such that if all letters are replaced simultaneously
a
a
a
to
a
b
a
aba
aba
and letters
b
b
b
to
b
b
a
bba
bba
does it transform into itself (possibly with a shift)? (A sequence is called periodic if there is such natural number
n
n
n
, which for every
i
=
1
,
2
,
.
.
.
i
i = 1, 2, . . . i
i
=
1
,
2
,
...
i
-th member of this sequence is equal to the (
i
+
n
i + n
i
+
n
)- th.)
combinatorics
periodic