MathDB

P2

Part of 2024 Romania Team Selection Tests

Problems(1)

Bashy min/max algebra

Source: Romania TST 2024 Day 1 P2

7/31/2024
Let n⩾2n\geqslant 2 be a fixed integer. Consider nn real numbers a1,a2,…,ana_1,a_2,\ldots,a_n not all equal and letd:=max⁡1⩽i<j⩽n∣ai−aj∣;s=∑1⩽i<j⩽n∣ai−aj∣.d:=\max_{1\leqslant i<j\leqslant n}|a_i-a_j|;\qquad s=\sum_{1\leqslant i<j\leqslant n}|a_i-a_j|.Determine in terms of nn{} the smalest and largest values the quotient s/ds/d may achieve.
Selected from the Kvant Magazine
algebrainequalities