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USA - Middle School Tournaments
LMT
2020 LMT Spring
5
5
Part of
2020 LMT Spring
Problems
(1)
Spring 2020 Team Round Problem 5
Source:
8/22/2020
For a positive integer
n
n
n
, let
D
(
n
)
\mathcal{D}(n)
D
(
n
)
be the value obtained by, starting from the left, alternating between adding and subtracting the digits of
n
n
n
. For example,
D
(
321
)
=
3
−
2
+
1
=
2
\mathcal{D}(321)=3-2+1=2
D
(
321
)
=
3
−
2
+
1
=
2
, while
D
(
40
)
=
4
−
0
=
4
\mathcal{D}(40)=4-0=4
D
(
40
)
=
4
−
0
=
4
. Compute the value of the sum
∑
n
=
1
100
D
(
n
)
=
D
(
1
)
+
D
(
2
)
+
⋯
+
D
(
100
)
.
\sum_{n=1}^{100}\mathcal{D}(n)=\mathcal{D}(1)+\mathcal{D}(2)+\dots+\mathcal{D}(100).
n
=
1
∑
100
D
(
n
)
=
D
(
1
)
+
D
(
2
)
+
⋯
+
D
(
100
)
.