English Issue, December 2002
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New exercises for practice - competition C
C. 690. Is it possible for the sum of the volumes of three cubes of integer edges to be 2002 units?
C. 691. Express in mm2 the area of Hungary on a globe of radius 25 cm.
C. 692. For the real numbers x, y, z,
x+2y+4z\(\displaystyle \ge\)3 and y-3x+2z \(\displaystyle \ge\)5.
Prove that y-x+2z\(\displaystyle \ge\)3.
C. 693. In what interval may the apex angle of an isosceles triangle vary if a triangle can be constructed out of its altitudes?
C. 694. Evaluate the sum [log21]+[log22]+[log23]+...+[log22002].
Suggested by Ádám Besenyei, Budapest