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Problems Algebra and arithmetic Algebraic equations and systems of equations Higher order equations. Palindromic polynomial equations Equations of higher order (other) Calculus Real numbers Integer and fractional parts. Archimedean property

2.0

In a group of friends, each two people have exactly five common acquaintances. Prove that the number of pairs of friends is divisible by 3.

Problem #PRU-64548

Problems Calculus Functions of one variable. Continuity Monotonicity, boundedness Algebra and arithmetic Algebraic inequalities and systems of inequalities Quadratic inequalites (several variables)

3.0

Find the largest value of the expression \(a + b + c + d - ab - bc - cd - da\), if each of the numbers \(a\), \(b\), \(c\) and \(d\) belongs to the interval \([0, 1]\).