IMO 1986 Shortlist
IMO 1986 Shortlist — 21 problems. 21 problems.
IMO 1986 Shortlist
21 problems · Source: IMO Compendium
Problems
| # | Origin | Problem |
|---|---|---|
| 1 | GBR | Find, with proof, all functions f defined on the nonnegative |
| 2 | SWE | Let f(x) = xn where n is a fixed positive integer and x = |
| 3 | USA | Let A, B, and C be three points on the edge of a circular |
| 4 | CZS | Let n be a positive integer and let p be a prime number, p > 3. |
| 5 | FRG | The set S = {2, 5, 13} has the property that for every |
| 6 | NET | Find four positive integers each not exceeding 70000 and each |
| 7 | FRA | Let real numbers x1, x2, . . . , xn satisfy 0 < x1 < x2 < \cdot \cdot \cdot < |
| 8 | USA | From a collection of n persons q distinct two-member teams |
| 9 | GDR | Prove or disprove: Given a finite set of points with integer |
| 10 | HUN | Three persons A, B, C, are playing the following game: A k- |
| 11 | BUL | Let f(n) be the least number of distinct points in the plane |
| 12 | GDR | To each vertex Pi (i = 1, . . . , 5) of a pentagon an integer |
| 13 | FRG | A particle moves from (0, 0) to (n, n) directed by a fair coin. |
| 14 | IRE | The circle inscribed in a triangle ABC touches the sides |
| 15 | NET | Let ABCD be a convex quadrilateral whose vertices do not |
| 16 | ISR | Let A, B be adjacent vertices of a regular n-gon in the |
| 17 | CHN | Let A, B, C be fixed points in the plane. A man starts |
| 18 | TUR | Let AX, BY, CZ be three cevians concurrent at an inte- |
| 19 | BUL | A tetrahedron ABCD is given such that AD = BC = a; |
| 20 | CAN | Prove that the sum of the face angles at each vertex of a tetra- |
| 21 | TUR | Let ABCD be a tetrahedron having each sum of opposite sides |