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Contests
National and Regional Contests
Belgium Contests
Flanders Math Olympiad
2002 Flanders Math Olympiad
2002 Flanders Math Olympiad
Part of
Flanders Math Olympiad
Subcontests
(4)
4
1
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shadow area
A lamp is situated at point
A
A
A
and shines inside the cube. A (massive) square is hung on the midpoints of the 4 vertical faces. What's the area of its shadow? http://www.mathlinks.ro/Forum/album_pic.php?pic_id=285
1
1
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[solved] - another challenge problem
Is it possible to number the
8
8
8
vertices of a cube from
1
1
1
to
8
8
8
in such a way that the value of the sum on every edge is different?
2
1
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easy functional equitation (Flanders '02)
Determine all functions
f
:
R
→
R
f: \mathbb{R}\rightarrow\mathbb{R}
f
:
R
→
R
so that
∀
x
:
x
⋅
f
(
x
2
)
−
f
(
2
x
)
=
1
\forall x: x\cdot f(\frac x2) - f(\frac2x) = 1
∀
x
:
x
⋅
f
(
2
x
)
−
f
(
x
2
)
=
1
3
1
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Numbers (Flanders '02)
show that
1
15
<
1
2
⋅
3
4
⋯
99
100
<
1
10
\frac1{15} < \frac12\cdot\frac34\cdots\frac{99}{100} < \frac1{10}
15
1
<
2
1
⋅
4
3
⋯
100
99
<
10
1