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Problems(3)
1997 MMO Grade 8 #1
Source:
10/3/2016
Some figures stand in certain cells of a chess board. It is known that a figure stands on each row, and that different rows have a different number of figures. Prove that it is possible to mark figures so that on each row and column stands exactly one marked figure.
Grade 81997
1997 MMO Grade 9 #1
Source:
10/3/2016
In a triangle one side is times shorter than the sum of the other two. Prove that the angle opposite said side is the smallest of the triangle’s angles.
Grade 91997
1997 MMO Grade 10 #1
Source:
10/3/2016
Is there a convex body distinct from ball whose three orthogonal projections on three pairwise perpendicular planes are discs?
Grade 101997