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National and Regional Contests
North Macedonia Contests
JBMO TST - Macedonia
2011 Junior Macedonian Mathematical Olympiad
1
1
Part of
2011 Junior Macedonian Mathematical Olympiad
Problems
(1)
classic problem
Source: Junior Macedonian MO 2011
10/5/2023
Let
S
(
n
)
S(n)
S
(
n
)
be the sum of digits of natural number
n
n{}
n
. Is there a natural number
n
n{}
n
for which
n
+
S
(
n
)
+
S
(
S
(
n
)
)
=
2011
?
n+S(n)+S(S(n))=2011?
n
+
S
(
n
)
+
S
(
S
(
n
))
=
2011
?