IMO 1973 Shortlist
IMO 1973 Shortlist — 17 problems. 17 problems.
IMO 1973 Shortlist
17 problems · Source: IMO Compendium
Problems
| # | Origin | Problem |
|---|---|---|
| 1 | BUL | Let a tetrahedron ABCD be inscribed in a sphere S. Find the |
| 2 | CZS | Given a circle K, find the locus of vertices A of parallelograms |
| 3 | CZS | Prove that the sum of an odd number of unit vectors passing |
| 4 | GBR | Let P be a set of 7 different prime numbers and C a set of |
| 5 | FRA | A circle of radius 1 is located in a right-angled trihedron and |
| 6 | POL | Does there exist a finite set M of points in space, not all in |
| 7 | POL | Given a tetrahedron ABCD, let x = AB \cdot CD, y = AC \cdot BD, |
| 8 | ROM | Prove that there are exactly |
| 9 | ROM | Let Ox, Oy, Oz be three rays, and G a point inside the trihe- |
| 10 | SWE | Let a1, a2, . . . , an be positive numbers and q a given real |
| 11 | SWE | Determine the minimum of a2 + b2 if a and b are real |
| 12 | SWE | Consider the two square matrices |
| 13 | YUG | Find the sphere of maximal radius that can be placed inside |
| 14 | YUG | A soldier has to investigate whether there are mines in an |
| 15 | CUB | Prove that for all n \inN the following is true: |
| 16 | CUB | Given a, \theta \inR, m \inN, and P(x) = x2m −2|a|mxm cos \theta+a2m, |
| 17 | POL | Let F be a nonempty set of functions f : R \toR of the |