IMO 1988 Shortlist
IMO 1988 Shortlist — 31 problems. 31 problems.
IMO 1988 Shortlist
31 problems · Source: IMO Compendium
Problems
| # | Origin | Problem |
|---|---|---|
| 1 | BUL | An integer sequence is defined by |
| 2 | BUL | Let n be a positive integer. Find the number of odd coefficients |
| 3 | CAN | The triangle ABC is inscribed in a circle. The interior bi- |
| 4 | CZS | An n \times n chessboard (n \geq2) is numbered by the numbers |
| 5 | CZS | Let n be an even positive integer. Let A1, A2, . . . , An+1 be |
| 6 | CZS | In a given tetrahedron ABCD let K and L be the centers of |
| 7 | FRA | Let a be the greatest positive root of the equation x3−3x2+1 = |
| 8 | FRA | Let u1, u2, . . . , um be m vectors in the plane, each of length |
| 9 | FRG | Let a and b be two positive integers such that ab+1 divides |
| 10 | GDR | Let N = {1, 2, . . ., n}, n \geq2. A collection F = {A1, . . . , At} |
| 11 | GDR | The lock on a safe consists of three wheels, each of which may |
| 12 | GRE | In a triangle ABC, choose any points K \inBC, L \inAC, |
| 13 | GRE | In a right-angled triangle ABC, let AD be the altitude |
| 14 | HUN | For what values of n does there exist an n \times n array of entries |
| 15 | ICE | Let ABC be an acute-angled triangle. Three lines LA, LB, |
| 16 | IRE | Show that the solution set of the inequality |
| 17 | ISR | In the convex pentagon ABCDE, the sides BC, CD, DE have |
| 18 | LUX | Consider two concentric circles of radii R and r (R > r) |
| 19 | MEX | Let f(n) be a function defined on the set of all positive integers |
| 20 | MON | Find the least natural number n such that if the set |
| 21 | POL | Forty-nine students solve a set of three problems. The score for |
| 22 | KOR | Let p be the product of two consecutive integers greater than |
| 23 | SIN | Let Q be the center of the inscribed circle of a triangle ABC. |
| 24 | SWE | Let {ak}\infty |
| 25 | GBR | A positive integer is called a double number if its decimal rep- |
| 26 | GBR | A function f defined on the positive integers (and taking |
| 27 | GBR | The triangle ABC is acute-angled. Let L be any line in the |
| 28 | GBR | The sequence {an} of integers is defined by a1 = 2, a2 = 7, |
| 29 | USA | A number of signal lights are equally spaced along a one-way |
| 30 | USS | A point M is chosen on the side AC of the triangle ABC in |
| 31 | USS | Around a circular table an even number of persons have a |