MathDB
Problems
Contests
International Contests
Tournament Of Towns
1988 Tournament Of Towns
(174) 7
(174) 7
Part of
1988 Tournament Of Towns
Problems
(1)
TOT 174 1988 Spring J7 words ABBAB
Source:
5/9/2020
Consider a sequence of words each consisting of two letters,
A
A
A
and
B
B
B
. The first word is "
A
A
A
" , while the second word is "
B
B
B
" . The
k
k
k
-th word is obtained from the (
k
−
2
k -2
k
−
2
)-nd by writing after it the (
k
−
1
k -1
k
−
1
)th one. (So the first few elements of the sequence are "
A
A
A
" , "
B
B
B
" ,"
A
B
AB
A
B
" , "
B
A
B
BAB
B
A
B
" , "
A
B
B
A
B
ABBAB
A
BB
A
B
" . ) Does there exist in this sequence a "periodical" word, i.e. a word of the form
P
P
P
.
.
.
P
P P P ... P
PPP
...
P
, where
P
P
P
is a word , repeated at least once? (Remark: For instance, the word
B
A
B
B
B
A
B
B
BABBBABB
B
A
BBB
A
BB
is of the form
P
P
PP
PP
, in which
P
P
P
is repeated exactly once . ) (A. Andjans, Riga)
combinatorics
Words