IMO 1970 Shortlist
IMO 1970 Shortlist — 12 problems. 12 problems.
IMO 1970 Shortlist
12 problems · Source: IMO Compendium
Problems
| # | Origin | Problem |
|---|---|---|
| 1 | BEL | Consider a regular 2n-gon and the n diagonals of it that |
| 2 | ROM | Let a and b be the bases of two number systems and let |
| 3 | BUL | In the tetrahedron SABC the angle BSC is a right angle, |
| 4 | CZS | For what natural numbers n can the product of some of |
| 5 | CZS | Let M be an interior point of the tetrahedron ABCD. Prove |
| 6 | FRA | In the triangle ABC let B′ and C′ be the midpoints of the sides |
| 7 | USS | For which digits a do exist integers n \geq4 such that each digit |
| 8 | POL | Given a point M on the side AB of the triangle ABC, let |
| 9 | GDR | Let u1, u2, . . . , un, v1, v2, . . . , vn be real numbers. Prove that |
| 10 | SWE | Let 1 = a0 \leqa1 \leqa2 \leq\cdot \cdot \cdot \leqan \leq\cdot \cdot \cdot be… |
| 11 | SWE | Let P, Q, R be polynomials and let S(x) = P(x3) + xQ(x3) + |
| 12 | USS | We are given 100 points in the plane, no three of which are |