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Problems
Contests
National and Regional Contests
Turkey Contests
National Olympiad First Round
2001 National Olympiad First Round
22
22
Part of
2001 National Olympiad First Round
Problems
(1)
P22 [Combinatorics] - Turkish NMO 1st Round - 2001
Source:
4/20/2014
A ladder is formed by removing some consecutive unit squares of a
10
×
10
10\times 10
10
×
10
chessboard such that for each
k
−
k-
k
−
th row (
k
∈
{
1
,
2
,
…
,
10
}
k\in \{1,2,\dots, 10\}
k
∈
{
1
,
2
,
…
,
10
}
), the leftmost
k
−
1
k-1
k
−
1
unit squares are removed. How many rectangles formed by composition of unit squares does the ladder have?
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
a
n
>
625
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
a
n
>
715
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
a
n
>
1024
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
a
n
>
1512
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
a
n
>
None of the preceding
<span class='latex-bold'>(A)</span>\ 625 \qquad<span class='latex-bold'>(B)</span>\ 715 \qquad<span class='latex-bold'>(C)</span>\ 1024 \qquad<span class='latex-bold'>(D)</span>\ 1512 \qquad<span class='latex-bold'>(E)</span>\ \text{None of the preceding}
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
an
>
625
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
an
>
715
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
an
>
1024
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
an
>
1512
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
an
>
None of the preceding
geometry
rectangle