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2024 Canadian Open Math Challenge
B3
2024 COMC B3
2024 COMC B3
Source:
November 4, 2024
Comc
Problem Statement
Let
a
,
b
,
c
,
d
a,b,c,d
a
,
b
,
c
,
d
be four distinct integers such that:
min
(
a
,
b
)
=
2
\text{min}(a,b)=2
min
(
a
,
b
)
=
2
min
(
b
,
c
)
=
0
\text{min}(b,c)=0
min
(
b
,
c
)
=
0
max
(
a
,
c
)
=
2
\text{max}(a,c)=2
max
(
a
,
c
)
=
2
max
(
c
,
d
)
=
4
\text{max}(c,d)=4
max
(
c
,
d
)
=
4
Here
min
(
a
,
b
)
\text{min}(a,b)
min
(
a
,
b
)
and
max
(
a
,
b
)
\text{max}(a,b)
max
(
a
,
b
)
denote respectively the minimum and the maximum of two numbers
a
a
a
and
b
b
b
. Determine the fifth smallest possible value for
a
+
b
+
c
+
d
a+b+c+d
a
+
b
+
c
+
d
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