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2021 CMIMC
2.1
2021 Alg/NT Div 2 P1
2021 Alg/NT Div 2 P1
Source:
March 2, 2021
algebra
number theory
Problem Statement
Find the unique 3 digit number
N
=
A
‾
N=\underline{A}
N
=
A
B
‾
\underline{B}
B
C
‾
,
\underline{C},
C
,
whose digits
(
A
,
B
,
C
)
(A, B, C)
(
A
,
B
,
C
)
are all nonzero, with the property that the product
P
=
A
‾
P=\underline{A}
P
=
A
B
‾
\underline{B}
B
C
‾
\underline{C}
C
×
\times
×
A
‾
\underline{A}
A
B
‾
\underline{B}
B
×
\times
×
A
‾
\underline{A}
A
is divisible by
1000
1000
1000
.Proposed by Kyle Lee
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