MathDB
Problems
Contests
National and Regional Contests
USA Contests
USA - College-Hosted Events
Harvard-MIT Mathematics Tournament
2007 Harvard-MIT Mathematics Tournament
10
2007 Guts #10: Difference of Base 10 Integers
2007 Guts #10: Difference of Base 10 Integers
Source:
June 22, 2012
Problem Statement
Let
A
12
A_{12}
A
12
denote the answer to problem
12
12
12
. There exists a unique triple of digits
(
B
,
C
,
D
)
(B,C,D)
(
B
,
C
,
D
)
such that
10
>
A
12
>
B
>
C
>
D
>
0
10>A_{12}>B>C>D>0
10
>
A
12
>
B
>
C
>
D
>
0
and
A
12
B
C
D
‾
−
D
C
B
A
12
‾
=
B
D
A
12
C
‾
,
\overline{A_{12}BCD}-\overline{DCBA_{12}}=\overline{BDA_{12}C},
A
12
BC
D
−
D
CB
A
12
=
B
D
A
12
C
,
where
A
12
B
C
D
‾
\overline{A_{12}BCD}
A
12
BC
D
denotes the four digit base
10
10
10
integer. Compute
B
+
C
+
D
B+C+D
B
+
C
+
D
.
Back to Problems
View on AoPS