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ASDAN Math Tournament
2016 ASDAN Math Tournament
16
16
Part of
2016 ASDAN Math Tournament
Problems
(1)
2016 Guts #16
Source:
8/14/2022
Let the notation
A
B
C
‾
\underline{ABC}
A
BC
denote the number compromised of the digits
A
A
A
,
B
B
B
, and
C
C
C
with
0
≤
A
,
B
,
C
≤
9
0\leq A,B,C\leq9
0
≤
A
,
B
,
C
≤
9
. That is,
A
B
C
‾
=
100
A
+
10
B
+
C
\underline{ABC}=100A+10B+C
A
BC
=
100
A
+
10
B
+
C
and
C
C
A
A
C
‾
=
10000
C
+
1000
C
+
100
A
+
10
A
+
C
\underline{CCAAC}=10000C+1000C+100A+10A+C
CC
AA
C
=
10000
C
+
1000
C
+
100
A
+
10
A
+
C
. Now, if
(
A
B
C
‾
)
2
=
C
C
A
A
C
‾
(\underline{ABC})^2=\underline{CCAAC}
(
A
BC
)
2
=
CC
AA
C
, where
A
A
A
,
B
B
B
, and
C
C
C
are distinct nonzero digits, find the
3
3
3
digit number
A
B
C
‾
\underline{ABC}
A
BC
.
2016
Guts Round