IMO 1982 Shortlist
IMO 1982 Shortlist — 20 problems. 20 problems.
IMO 1982 Shortlist
20 problems · Source: IMO Compendium
Problems
| # | Origin | Problem |
|---|---|---|
| 1 | — | A1 (GBR 3)IMO1 The function f(n) is defined for all positive integers |
| 2 | — | A2 (YUG 1) Let K be a convex polygon in the plane and suppose that |
| 3 | — | A3 (USS 4)IMO3 Consider the infinite sequences {xn} of positive real |
| 4 | — | A4 (BUL 2) Determine all real values of the parameter a for which the |
| 5 | — | A5 (NET 2)IMO5 Let A1A2A3A4A5A6 be a regular hexagon. Each of its |
| 6 | — | A6 (VIE 1)IMO6 Let S be a square with sides of length 100 and let L be |
| 7 | — | B1 (CAN 2) |
| 8 | — | B2 (POL 4) A convex, closed figure lies inside a given circle. The figure |
| 9 | — | B3 (GBR 1) Let ABC be a triangle, and let P be a point inside it such |
| 10 | — | B4 (BRA 1) A box contains p white balls and q black balls. Beside the |
| 11 | — | B5 (CAN 3) |
| 12 | — | B6 (FIN 3) Four distinct circles C, C1, C2, C3 and a line L are given in |
| 13 | — | C1 (NET 1)IMO2 A scalene triangle A1A2A3 is given with sides a1, a2, a3 |
| 14 | — | C2 (AUS 4) |
| 15 | — | C3 (CAN 5) Show that |
| 16 | — | C4 (GBR 2)IMO4 Prove that if n is a positive integer such that the |
| 17 | — | C5 (USS 5) The right triangles ABC and AB1C1 are similar and have |
| 18 | — | C6 (FRA 2) Let O be a point of three-dimensional space and let l1, l2, l3 |
| 19 | — | C7 (CZS 3) |
| 20 | — | C8 (TUN 3) Let ABCD be a convex quadrilateral and draw regular tri- |