IMO 1976 Shortlist
IMO 1976 Shortlist — 12 problems. 12 problems.
IMO 1976 Shortlist
12 problems · Source: IMO Compendium
Problems
| # | Origin | Problem |
|---|---|---|
| 1 | BUL | Let ABC be a triangle with bisectors AA1, BB1, CC1 (A1 \in |
| 2 | BUL | Let a0, a1, . . . , an, an+1 be a sequence of real numbers satisfying |
| 3 | CZS | In a convex quadrangle with area 32 cm2, the sum of the |
| 4 | — | (GBR 1a)IMO6 For all positive integral n, un+1 = un(u2 |
| 5 | NET | Let a set of p equations be given, |
| 6 | NET | A rectangular box can be filled completely with unit cubes. |
| 7 | — | (POL 1b) Let I = (0, 1] be the unit interval of the real line. For a given |
| 8 | SWE | Let P be a polynomial with real coefficients such that P(x) > 0 |
| 9 | FIN | Let P1(x) = x2 −2, Pj(x) = P1(Pj−1(x)), j = 2, 3, . . . . |
| 10 | USA | Find the largest number obtainable as the product of pos- |
| 11 | VIE | Prove that there exist infinitely many positive integers n such |
| 12 | VIE | The polynomial 1976(x+x2+\cdot \cdot \cdot+xn) is decomposed into a sum |