MathDB
Problems
Contests
National and Regional Contests
Turkey Contests
Turkey Junior National Olympiad
2001 Turkey Junior National Olympiad
2001 Turkey Junior National Olympiad
Part of
Turkey Junior National Olympiad
Subcontests
(3)
3
1
Hide problems
Turkey Junior Olympiad 2001, Part II - P3
11
11
11
carriers will carry
270
270
270
kg of melons at one step where each melons weighs at most
7
7
7
kg. Each carrier can carry at most
30
30
30
kg in one step. Show that it is possible to carry all the melons at one step whatever a melon weighs.
2
1
Hide problems
Turkey Junior Olympiad 2001, Part II - P2
Let
N
>
1
N>1
N
>
1
be an integer. We are adding all remainders when we divide
N
N
N
by all positive integers less than
N
N
N
. If this sum is less than
N
N
N
, find all possible values of
N
N
N
.
1
1
Hide problems
Turkey Junior Olympiad 2001, Part II - P1
Let
A
B
C
D
ABCD
A
BC
D
be an inscribed trapezoid such that the sides
[
A
B
]
[AB]
[
A
B
]
and
[
C
D
]
[CD]
[
C
D
]
are parallel. If
m
(
A
O
D
^
)
=
6
0
∘
m(\widehat{AOD})=60^\circ
m
(
A
O
D
)
=
6
0
∘
and the altitude of the trapezoid is
10
10
10
, what is the area of the trapezoid?