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2021 LMT Spring
B13
B13
Part of
2021 LMT Spring
Problems
(1)
2021 Spring LMT Division B Problem 13
Source:
1/22/2022
Call a
4
4
4
-digit number
a
b
c
d
‾
\overline{a b c d}
ab
c
d
unnoticeable if
a
+
c
=
b
+
d
a +c = b +d
a
+
c
=
b
+
d
and
a
b
c
d
‾
+
c
d
a
b
‾
\overline{a b c d} +\overline{c d a b}
ab
c
d
+
c
d
ab
is a multiple of
7
7
7
. Find the number of unnoticeable numbers.Note:
a
a
a
,
b
b
b
,
c
c
c
, and
d
d
d
are nonzero distinct digits.Proposed by Aditya Rao
number theory