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National and Regional Contests
India Contests
India Pre-Regional Mathematical Olympiad
2019 India PRMO
7
Sum of digits
Sum of digits
Source: PRMO 2019 Leg 2 P7
August 25, 2019
algebra
PRMO
number theory
decimal representation
Problem Statement
Let
s
(
n
)
s(n)
s
(
n
)
denote the sum of digits of a positive integer
n
n
n
in base
10
10
10
. If
s
(
m
)
=
20
s(m)=20
s
(
m
)
=
20
and
s
(
33
m
)
=
120
s(33m)=120
s
(
33
m
)
=
120
, what is the value of
s
(
3
m
)
s(3m)
s
(
3
m
)
?
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