IMO 1978 Shortlist
IMO 1978 Shortlist — 17 problems. 17 problems.
IMO 1978 Shortlist
17 problems · Source: IMO Compendium
Problems
| # | Origin | Problem |
|---|---|---|
| 1 | BUL | The set M = {1, 2, . . ., 2n} is partitioned into k nonintersecting |
| 2 | BUL | Two identically oriented equilateral triangles, ABC with center |
| 3 | CUB | Let n > m \geq1 be natural numbers such that the groups of |
| 4 | CZS | Let T1 be a triangle having a, b, c as lengths of its sides and let |
| 5 | GDR | For every integer d \geq1, let Md be the set of all positive |
| 6 | FRA | Let ϕ : {1, 2, 3, . . .} … be injective. Prove that |
| 7 | FRA | We consider three distinct half-lines Ox, Oy, Oz in a plane. |
| 8 | GBR | Let S be the set of all the odd positive integers that are not |
| 9 | GBR | Let {f(n)} be a strictly increasing sequence of positive |
| 10 | NET | An international society has its members in 6 different |
| 11 | SWE | A function f : I \toR, defined on an interval I, is called |
| 12 | USA | In a triangle ABC we have AB = AC. A circle is tangent |
| 13 | USA | Given any point P in the interior of a sphere with ra- |
| 14 | VIE | Prove that it is possible to place 2n(2n + 1) parallelepipedic |
| 15 | YUG | Let p be a prime and A = {a1, . . . , ap−1} an arbitrary subset |
| 16 | YUG | Determine all the triples (a, b, c) of positive real numbers such |
| 17 | FRA | Prove that for any positive integers x, y, z with xy−z2 = 1 one |