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Problems
Contests
National and Regional Contests
Belgium Contests
Flanders Math Olympiad
2008 Flanders Math Olympiad
2008 Flanders Math Olympiad
Part of
Flanders Math Olympiad
Subcontests
(4)
3
1
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gluing a quadrilateral pyramid with a regular tetrahedron of equal edges
A quadrilateral pyramid and a regular tetrahedron have edges that are all equal in length. They are glued together so that they have in common
1
1
1
equilateral triangle . Prove that the resulting body has exactly
5
5
5
sides.
2
1
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1/2(a^4 +b^4 +c^4) is pefrect square if a+b+c = 0
Let
a
,
b
a, b
a
,
b
and
c
c
c
be integers such that
a
+
b
+
c
=
0
a+b+c = 0
a
+
b
+
c
=
0
. Prove that
1
2
(
a
4
+
b
4
+
c
4
)
\frac12(a^4 +b^4 +c^4)
2
1
(
a
4
+
b
4
+
c
4
)
is a perfect square.
1
1
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4-digit number wanted
Determine all natural numbers
n
n
n
of
4
4
4
digits whose quadruple minus the number formed by the digits of
n
n
n
in reverse order equals
30
30
30
.
4
1
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area wanted, 4 equal circles inside a square (2008 VWO Flanders MO p4)
A square with sides
1
1
1
and four circles of radius
1
1
1
considered each having a vertex of have the square as the center. Find area of the shaded part (see figure). https://cdn.artofproblemsolving.com/attachments/b/6/6e28d94094d69bac13c2702853ac2c906a80a1.png