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Contests
National and Regional Contests
Paraguay Contests
Paraguay Mathematical Olympiad
2001 Paraguay Mathematical Olympiad
2001 Paraguay Mathematical Olympiad
Part of
Paraguay Mathematical Olympiad
Subcontests
(4)
4
1
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area chasing in a parallelogram OMAPA Paraguay 2001.4
In a parallelogram
A
B
C
D
ABCD
A
BC
D
of surface area
60
60
60
cm
2
^2
2
, a line is drawn by
D
D
D
that intersects
B
C
BC
BC
at
P
P
P
and the extension of
A
B
AB
A
B
at
Q
Q
Q
. If the area of the quadrilateral
A
B
P
D
ABPD
A
BP
D
is
46
46
46
cm
2
^2
2
, find the area of triangle
C
P
Q
CPQ
CPQ
.
3
1
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10digit numbers, divisible by sum of digits OMAPA Paraguay 2001.3
Find a
10
10
10
-digit number, in which no digit is zero, that is divisible by the sum of their digits.
2
1
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min 4digit =1 mod2, mod3, mod4, mod5, mod6 OMAPA Paraguay 2001.2
Find the four smallest four-digit numbers that meet the following condition: by dividing by
2
2
2
,
3
3
3
,
4
4
4
,
5
5
5
or
6
6
6
the remainder is
1
1
1
.
1
1
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different towers by cans of 4 colors OMAPA Paraguay 2001.1
In a warehouse there are many empty cans of
4
4
4
colors: red, green, Blue and yellow. Some boys play to build towers in which no two cans of the same color, with a can in each floor and at any height. How many different towers can be built?