IMO 1981 Shortlist
IMO 1981 Shortlist — 19 problems. 19 problems.
IMO 1981 Shortlist
19 problems · Source: IMO Compendium
Problems
| # | Origin | Problem |
|---|---|---|
| 1 | BEL | (a) For which values of n > 2 is there a set of n consecutive |
| 2 | BUL | A sphere S is tangent to the edges AB, BC, CD, DA of a tetrahe- |
| 3 | CAN | Find the minimum value of |
| 4 | CAN | Let {fn} be the Fibonacci sequence {1, 1, 2, 3, 5, . . .}. |
| 5 | COL | A cube is assembled with 27 white cubes. The larger cube is then |
| 6 | CUB | Let P(z) and Q(z) be complex-variable polynomials, with degree |
| 7 | FIN | Assume that f(x, y) is defined for all positive integers x and |
| 8 | FRG | Let f(n, r) be the arithmetic mean of the minima of all r- |
| 9 | FRG | A sequence (an) is defined by means of the recursion |
| 10 | FRA | Determine the smallest natural number n having the following |
| 11 | NET | On a semicircle with unit radius four consecutive chords AB, BC, |
| 12 | NET | Determine the maximum value of m2 + n2 where m and n |
| 13 | ROM | Let P be a polynomial of degree n satisfying |
| 14 | ROM | Prove that a convex pentagon (a five-sided polygon) ABCDE |
| 15 | GBR | Find the point P inside the triangle ABC for which |
| 16 | GBR | A sequence of real numbers u1, u2, u3, . . . is determined by u1 |
| 17 | USS | Three equal circles touch the sides of a triangle and have |
| 18 | USS | Several equal spherical planets are given in outer space. On the |
| 19 | YUG | A finite set of unit circles is given in a plane such that the area |