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MAA AMC
AMC 10
2017 AMC 10
1
Complicated Calculations
Complicated Calculations
Source: 2017 AMC 10A #1
February 8, 2017
AMC
AMC 10
AMC 10 A
2017 AMC 10A
Problem Statement
What is the value of
2
(
2
(
2
(
2
(
2
(
2
+
1
)
+
1
)
+
1
)
+
1
)
+
1
)
+
1
2(2(2(2(2(2+1)+1)+1)+1)+1)+1
2
(
2
(
2
(
2
(
2
(
2
+
1
)
+
1
)
+
1
)
+
1
)
+
1
)
+
1
?
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
a
n
>
70
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
a
n
>
97
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
a
n
>
127
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
a
n
>
159
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
a
n
>
729
<span class='latex-bold'>(A) </span> 70 \qquad <span class='latex-bold'>(B) </span> 97 \qquad <span class='latex-bold'>(C) </span> 127 \qquad <span class='latex-bold'>(D) </span> 159 \qquad <span class='latex-bold'>(E) </span> 729
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
an
>
70
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
an
>
97
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
an
>
127
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
an
>
159
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
an
>
729
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