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El Salvador Contests
El Salvador Correspondence
2008 El Salvador Correspondence
2008 El Salvador Correspondence
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El Salvador Correspondence
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2008 El Salvador Correspondence / Qualifying NMO VIII
p1. Figures
0
0
0
,
1
1
1
,
2
2
2
and
3
3
3
consist of
1
1
1
,
5
5
5
,
13
13
13
and
25
25
25
squares. If you continue with this scheme, define how many squares figure
100
100
100
has. https://cdn.artofproblemsolving.com/attachments/2/1/ffc1675513e285e51881b6ef54aa5fb2640605.png p2. The figure shows
5
5
5
scales with objects and the total weights in each of them: https://cdn.artofproblemsolving.com/attachments/d/5/4408d9f3ae40b5fcb4c5e30941b699bffd65ed.png One of the scales malfunctions and the other
4
4
4
indicate the correct weight. Determine which scale is malfunctioning and enter the weights of each object :
⧫
\blacklozenge
⧫
,
∙
\bullet
∙
,
□
\Box
□
p3. The positive real numbers
a
a
a
and
b
b
b
satisfy the relation
a
b
=
a
−
b
ab = a-b
ab
=
a
−
b
. Find the value of
a
/
b
+
b
/
a
−
a
b
a/b + b/a - ab
a
/
b
+
b
/
a
−
ab
. p4. Let
A
B
C
D
ABCD
A
BC
D
be a square of area
1
1
1
. Let
P
P
P
and
Q
Q
Q
be points outside the square such that the triangles
A
B
P
ABP
A
BP
and
B
C
Q
BCQ
BCQ
are equilateral. Find the area of the triangle
P
B
Q
PBQ
PBQ
. p5. Place different natural numbers greater than
1
1
1
in the boxes, so that each number is a multiple of the number written in the box to its left, and that the sum of the five numbers is
517
517
517
. https://cdn.artofproblemsolving.com/attachments/6/3/8257ecdaac09b73186e9c84b26668d5b26e413.png