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Contests
National and Regional Contests
Belgium Contests
Flanders Junior Olympiad
2002 Flanders Junior Olympiad
2002 Flanders Junior Olympiad
Part of
Flanders Junior Olympiad
Subcontests
(3)
4
1
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Sliding triangles
Two congruent right-angled isosceles triangles (with baselength 1) slide on a line as on the picture. What is the maximal area of overlap? http://www.mathlinks.ro/Forum/album_pic.php?pic_id=287
1
1
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inequality - well known
Prove that for all
a
,
b
,
c
∈
R
0
+
a,b,c \in \mathbb{R}^+_0
a
,
b
,
c
∈
R
0
+
we have
a
b
c
+
b
a
c
+
c
a
b
≥
2
a
+
2
b
−
2
c
\frac{a}{bc}+\frac{b}{ac}+\frac{c}{ab} \ge \frac2a+\frac2b-\frac2c
b
c
a
+
a
c
b
+
ab
c
≥
a
2
+
b
2
−
c
2
and determine when equality occurs.
2
1
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[To be solved] - Challenge Problem: number array
Prove that there are no perfect squares in the array below:
11
111
1111
.
.
.
22
222
2222
.
.
.
33
333
3333
.
.
.
44
444
4444
.
.
.
55
555
5555
.
.
.
66
666
6666
.
.
.
77
777
7777
.
.
.
88
888
8888
.
.
.
99
999
9999
.
.
.
\begin{array}{cccc}11&111&1111&...\\22&222&2222&...\\33&333&3333&...\\44&444&4444&...\\55&555&5555&... \\66&666&6666&...\\77&777&7777&...\\88&888&8888&...\\99&999&9999&...\end{array}
11
22
33
44
55
66
77
88
99
111
222
333
444
555
666
777
888
999
1111
2222
3333
4444
5555
6666
7777
8888
9999
...
...
...
...
...
...
...
...
...