On a field, there are two pegs, \(A\) and \(B\), placed \(15\) metres apart. Each peg has a small ring placed on top, and a rope can slide freely through these rings.
You have one rope and two goats that want to graze the grass - but they will fight each other if they can both reach the same spot. For what lengths of rope can you arrange things so that the goats cannot reach each other?