MathDB
Problems
Contests
National and Regional Contests
Bosnia Herzegovina Contests
Bosnia And Herzegovina - Regional Olympiad
2014 Bosnia And Herzegovina - Regional Olympiad
2014 Bosnia And Herzegovina - Regional Olympiad
Part of
Bosnia And Herzegovina - Regional Olympiad
Subcontests
(4)
4
3
Hide problems
Regional Olympiad - FBH 2014 Grade 9 Problem 4
Determine the set
S
S
S
with minimal number of points defining
7
7
7
distinct lines
Regional Olympiad - FBH 2014 Grade 10 Problem 4
How namy subsets with
3
3
3
elements of set
S
=
{
1
,
2
,
3
,
.
.
.
,
19
,
20
}
S=\{1,2,3,...,19,20\}
S
=
{
1
,
2
,
3
,
...
,
19
,
20
}
exist, such that their product is divisible by
4
4
4
.
Regional Olympiad - FBH 2014 Grade 11 Problem 4
At the beginning of school year in one of the first grade classes:
i
)
i)
i
)
every student had exatly
20
20
20
acquaintances
i
i
)
ii)
ii
)
every two students knowing each other had exactly
13
13
13
mutual acquaintances
i
i
i
)
iii)
iii
)
every two students not knowing each other had exactly
12
12
12
mutual acquaintances Find number of students in this class
2
3
Hide problems
Regional Olympiad - FBH 2014 Grade 9 Problem 2
Solve the equation, where
x
x
x
and
y
y
y
are positive integers:
x
3
−
y
3
=
999
x^3-y^3=999
x
3
−
y
3
=
999
Regional Olympiad - FBH 2014 Grade 10 Problem 2
Let
a
a
a
,
b
b
b
and
c
c
c
be positive real numbers such that
a
b
+
b
c
+
c
a
=
1
ab+bc+ca=1
ab
+
b
c
+
c
a
=
1
. Prove the inequality:
1
a
+
1
b
+
1
c
≥
3
(
a
+
b
+
c
)
\frac{1}{a}+\frac{1}{b}+\frac{1}{c} \geq 3(a+b+c)
a
1
+
b
1
+
c
1
≥
3
(
a
+
b
+
c
)
Regional Olympiad - FBH 2014 Grade 11 Problem 2
Solve the equation
x
2
+
y
2
+
z
2
=
686
x^2+y^2+z^2=686
x
2
+
y
2
+
z
2
=
686
where
x
x
x
,
y
y
y
and
z
z
z
are positive integers
1
4
Show problems
3
4
Show problems