IMO Shortlist 2009 problem C8
Kvaliteta:
Avg: 0,0Težina:
Avg: 9,0 For any integer
, we compute the integer
by applying the following procedure to its decimal representation. Let
be the rightmost digit of
.
If
, then the decimal representation of
results from the decimal representation of
by removing this rightmost digit
.If
we split the decimal representation of
into a maximal right part
that solely consists of digits not less than
and into a left part
that either is empty or ends with a digit strictly smaller than
. Then the decimal representation of
consists of the decimal representation of
, followed by two copies of the decimal representation of
. For instance, for the number
, we will have
,
and
.Prove that, starting with an arbitrary integer
, iterated application of
produces the integer
after finitely many steps.
Proposed by Gerhard Woeginger, Austria




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Proposed by Gerhard Woeginger, Austria
Izvor: Međunarodna matematička olimpijada, shortlist 2009