A Minimax of Four Absolutes

Problem

Let $M$ be the largest of the four numbers

|a+b|, \quad |a-b|, \quad |a-c|, \quad |b-d|.

Given that $c + d \geqslant 2$ , find the minimum possible value of $M$ .

Answer

Solution

Difficulty	7/10
Topics	Absolute Value, algebra, inequality

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