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1999 AIME Problems
5
Digital Sum
Digital Sum
Source:
December 18, 2005
Problem Statement
For any positive integer
x
x
x
, let
S
(
x
)
S(x)
S
(
x
)
be the sum of the digits of
x
x
x
, and let
T
(
x
)
T(x)
T
(
x
)
be
∣
S
(
x
+
2
)
−
S
(
x
)
∣
.
|S(x+2)-S(x)|.
∣
S
(
x
+
2
)
−
S
(
x
)
∣.
For example,
T
(
199
)
=
∣
S
(
201
)
−
S
(
199
)
∣
=
∣
3
−
19
∣
=
16.
T(199)=|S(201)-S(199)|=|3-19|=16.
T
(
199
)
=
∣
S
(
201
)
−
S
(
199
)
∣
=
∣3
−
19∣
=
16.
How many values
T
(
x
)
T(x)
T
(
x
)
do not exceed 1999?
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