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2016 SDMO (Middle School)
1
1
Part of
2016 SDMO (Middle School)
Problems
(1)
Clover convolution
Source: 2016 SDMO Middle School Problem 1
8/25/2016
Let
♣
(
x
)
\clubsuit\left(x\right)
♣
(
x
)
denote the sum of the digits of the positive integer
x
x
x
. For example,
♣
(
8
)
=
8
\clubsuit\left(8\right)=8
♣
(
8
)
=
8
and
♣
(
123
)
=
1
+
2
+
3
=
6
\clubsuit\left(123\right)=1+2+3=6
♣
(
123
)
=
1
+
2
+
3
=
6
. For how many two-digit values of
x
x
x
is
♣
(
♣
(
x
)
)
=
3
\clubsuit\left(\clubsuit\left(x\right)\right)=3
♣
(
♣
(
x
)
)
=
3
?
real analysis