Y by junioragd
Given a sequence
consisting of digits
and
. For any positive integer
, define
the maximum number of ways in any sequence of length
that several consecutive digits can be identified, forming the sequence
. (For example, if
, then
, because in sequences
and
one can find consecutive digits
in two places, and three pairs of
cannot meet in a sequence of length
or
.) It is known that
for some positive integer
. Prove that in the sequence
, all the numbers are the same.
A. Golovanov


















A. Golovanov