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Problems
Contests
National and Regional Contests
Canada Contests
Canadian Open Math Challenge
2018 Canadian Open Math Challenge
B3
B3
Part of
2018 Canadian Open Math Challenge
Problems
(1)
2018 COMC B3
Source:
12/6/2018
Source: 2018 Canadian Open Math Challenge Part B Problem 3 —--The doubling sum function is defined by
D
(
a
,
n
)
=
a
+
2
a
+
4
a
+
8
a
+
.
.
.
⏞
n terms
.
D(a,n)=\overbrace{a+2a+4a+8a+...}^{\text{n terms}}.
D
(
a
,
n
)
=
a
+
2
a
+
4
a
+
8
a
+
...
n terms
.
For example, we have
D
(
5
,
3
)
=
5
+
10
+
20
=
35
D(5,3)=5+10+20=35
D
(
5
,
3
)
=
5
+
10
+
20
=
35
and
D
(
11
,
5
)
=
11
+
22
+
44
+
88
+
176
=
341.
D(11,5)=11+22+44+88+176=341.
D
(
11
,
5
)
=
11
+
22
+
44
+
88
+
176
=
341.
Determine the smallest positive integer
n
n
n
such that for every integer
i
i
i
between
1
1
1
and
6
6
6
, inclusive, there exists a positive integer
a
i
a_i
a
i
such that
D
(
a
i
,
i
)
=
n
.
D(a_i,i)=n.
D
(
a
i
,
i
)
=
n
.
Comc
2018 COMC