Problem #PRU-109685

Problems Algebra Methods Algebraic inequalities and systems of inequalities Real numbers Rational and irrational numbers Linear inequalites and systems of inequalities Proof by contradiction Calculus
 14–16  4.0

Problem

At all rational points of the real line, integers are arranged. Prove that there is a segment such that the sum of the numbers at its ends does not exceed twice the number on its middle.