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CMIMC Problems
2022 CMIMC
9
9
Part of
2022 CMIMC
Problems
(1)
2022 Team P9
Source:
2/28/2022
For natural numbers
n
n
n
, let
r
(
n
)
r(n)
r
(
n
)
be the number formed by reversing the digits of
n
n
n
, and take
f
(
n
)
f(n)
f
(
n
)
to be the maximum value of
r
(
k
)
k
\frac{r(k)}k
k
r
(
k
)
across all
n
n
n
-digit positive integers
k
k
k
. If we define
g
(
n
)
=
⌊
1
10
−
f
(
n
)
⌋
g(n)=\left\lfloor\frac1{10-f(n)}\right\rfloor
g
(
n
)
=
⌊
10
−
f
(
n
)
1
⌋
, what is the value of
g
(
20
)
g(20)
g
(
20
)
? Proposed by Adam Bertelli
team