The 11th Balkan Mathematical Olympiad
1994年第11届巴尔干地区数学奥林匹克 |
- Given a point P inside an acute angle XAY, show how to construct a line through P meeting the line AX at B and the line AY at C such that the area of the triangle ABC is AP2.
- Show that x4 - 1993 x3 + (1993 + n) x2 - 11x + n = 0 has at most one integer root if n is an integer.
- What is the maximum value f(n) of |s1 - s2| + |s2 - s3| + ... + |sn-1 - sn| over all permutations s1, s2, ... , sn of 1, 2, ... , n ?
- Find the smallest n > 4 for which we can find a graph on n points with no triangles and such that for every two unjoined points we can find just two points joined to both of them.
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