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Bosnia And Herzegovina - Regional Olympiad
2013 Bosnia And Herzegovina - Regional Olympiad
2013 Bosnia And Herzegovina - Regional Olympiad
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Bosnia And Herzegovina - Regional Olympiad
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Regional Olympiad - FBH 2013 Grade 9 Problem 4
a
)
a)
a
)
Is it possible, on modified chessboard
20
×
30
20 \times 30
20
×
30
, to draw a line which cuts exactly
50
50
50
cells where chessboard cells are squares
1
×
1
1 \times 1
1
×
1
b
)
b)
b
)
What is the maximum number of cells which line can cut on chessboard
m
×
n
m \times n
m
×
n
,
m
,
n
∈
N
m,n \in \mathbb{N}
m
,
n
∈
N
Regional Olympiad - FBH 2013 Grade 11 Problem 4
If
A
=
{
1
,
2
,
.
.
.
,
4
s
−
1
,
4
s
}
A=\{1,2,...,4s-1,4s\}
A
=
{
1
,
2
,
...
,
4
s
−
1
,
4
s
}
and
S
⊆
A
S \subseteq A
S
⊆
A
such that
∣
S
∣
=
2
s
+
2
\mid S \mid =2s+2
∣
S
∣=
2
s
+
2
, prove that in
S
S
S
we can find three distinct numbers
x
x
x
,
y
y
y
and
z
z
z
such that
x
+
y
=
2
z
x+y=2z
x
+
y
=
2
z
3
2
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Regional Olympiad - FBH 2013 Grade 10 Problem 3
Find all integers
a
a
a
such that
9
a
+
4
a
−
6
\sqrt{\frac{9a+4}{a-6}}
a
−
6
9
a
+
4
is rational number
Regional Olympiad - FBH 2013 Grade 9 Problem 3
Find maximal positive integer
p
p
p
such that
5
7
5^7
5
7
is sum of
p
p
p
consecutive positive integers
2
4
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