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2016 Online Math Open Problems
9
9
Part of
2016 Online Math Open Problems
Problems
(2)
2015-2016 Spring OMO #9
Source:
3/29/2016
Let
f
(
n
)
=
1
×
3
×
5
×
⋯
×
(
2
n
−
1
)
f(n)=1 \times 3 \times 5 \times \cdots \times (2n-1)
f
(
n
)
=
1
×
3
×
5
×
⋯
×
(
2
n
−
1
)
. Compute the remainder when
f
(
1
)
+
f
(
2
)
+
f
(
3
)
+
⋯
+
f
(
2016
)
f(1)+f(2)+f(3)+\cdots +f(2016)
f
(
1
)
+
f
(
2
)
+
f
(
3
)
+
⋯
+
f
(
2016
)
is divided by
100.
100.
100.
Proposed by James Lin
Online Math Open
2016-2017 Fall OMO Problem 9
Source:
11/16/2016
In quadrilateral
A
B
C
D
ABCD
A
BC
D
,
A
B
=
7
,
B
C
=
24
,
C
D
=
15
,
D
A
=
20
,
AB=7, BC=24, CD=15, DA=20,
A
B
=
7
,
BC
=
24
,
C
D
=
15
,
D
A
=
20
,
and
A
C
=
25
AC=25
A
C
=
25
. Let segments
A
C
AC
A
C
and
B
D
BD
B
D
intersect at
E
E
E
. What is the length of
E
C
EC
EC
?Proposed by James Lin
Online Math Open
geometry