Rmo 1993 Solutions Jun 2026

Take any line not parallel to any line through two points. Start with all points on one side. Rotate the line until it passes through a point. Each time the line passes a point, the count changes by 1.

The 1993 Regional Mathematical Olympiad (RMO) remains a significant milestone for students preparing for the Indian National Mathematical Olympiad (INMO) . The paper features a classic mix of geometry, number theory, and combinatorics, challenging students to think beyond standard school formulas.

We need ( n^2 + 1 \mid n! ).

$$AI^2 = r(r + 2R)$$

For ( n \leq 4 ), test directly:

Ten persons each write down the sum of the ages of the other nine. The results are . One sum is repeated. Find the individual ages. Solution: Identify the Repeated Sum: Let be the sum of all 10 ages. Each person's written sum is . The total of all 10 written sums must be

However, we need to consider the restrictions $1 \le x_i \le 5$. rmo 1993 solutions

Let $f(x) = x^2 + 2x + 1$. Find the range of $f(x)$ for $x \in [-2, 2]$.

[ \fracBEEA \cdot \fracADDC? \text No, Menelaus: \fracBEEA \cdot \fracAFFC \cdot \fracCDDB = 1 ] Take any line not parallel to any line through two points