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National and Regional Contests
Belgium Contests
Flanders Junior Olympiad
2003 Flanders Junior Olympiad
2003 Flanders Junior Olympiad
Part of
Flanders Junior Olympiad
Subcontests
(3)
4
1
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lattice points
The points in the plane with integer coordinates are numbered as below. http://www.mathlinks.ro/Forum/album_pic.php?pic_id=288 What are the coordinates of the number
2003
2003
2003
?
2
1
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sum of ratios
Through an internal point
O
O
O
of
Δ
A
B
C
\Delta ABC
Δ
A
BC
one draws 3 lines, parallel to each of the sides, intersecting in the points shown on the picture. http://www.mathlinks.ro/Forum/album_pic.php?pic_id=289 Find the value of
∣
A
F
∣
∣
A
B
∣
+
∣
B
E
∣
∣
B
C
∣
+
∣
C
N
∣
∣
C
A
∣
\frac{|AF|}{|AB|}+\frac{|BE|}{|BC|}+\frac{|CN|}{|CA|}
∣
A
B
∣
∣
A
F
∣
+
∣
BC
∣
∣
BE
∣
+
∣
C
A
∣
∣
CN
∣
.
3
1
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birthday
Yesterday (=April 22, 2003) was Gittes birthday. She notices that her age equals the sum of the 4 digits of the year she was born in. How old is she?