IMO 1975 Shortlist
IMO 1975 Shortlist — 15 problems. 15 problems.
IMO 1975 Shortlist
15 problems · Source: IMO Compendium
Problems
| # | Origin | Problem |
|---|---|---|
| 1 | FRA | There are six ports on a lake. Is it possible to organize a series |
| 2 | CZS | Let x1 \geqx2 \geq\cdot \cdot \cdot \geqxn and y1 \geqy2 \geq\cdot \cdot \cdot… |
| 3 | USA | Find the integer represented by |
| 4 | SWE | Let a1, a2, . . . , an, . . . be a sequence of real numbers such that |
| 5 | SWE | Let M be the set of all positive integers that do not contain the |
| 6 | USS | Let A be the sum of the digits of the number 1616 and B |
| 7 | GDR | Prove that from x + y = 1 (x, y \inR) it follows that |
| 8 | NET | On the sides of an arbitrary triangle ABC, triangles BPC, |
| 9 | NET | Let f(x) be a continuous function defined on the closed interval |
| 10 | GBR | The function f(x, y) is a homogeneous polynomial of the nth |
| 11 | GBR | Let a1, a2, a3, . . . be any infinite increasing sequence of pos- |
| 12 | GRE | Consider on the first quadrant of the trigonometric circle the |
| 13 | ROM | Let A0, A1, . . . , An be points in a plane such that |
| 14 | YUG | Let x0 = 5 and xn+1 = xn + |
| 15 | USS | Is it possible to plot 1975 points on a circle with radius 1 so |