You are given two containers, the first containing one litre ofwine and the second one litre of water. You also have a cup whichhas a capacity of r litres, where 0 < r < 1. You fill the cupfrom the first container and transfer the content to the secondcontainer, stirring thoroughly afterwards. Next, dip the cup in thesecond container and transfer r litres of liquid back to the firstcontainer. This operation is repeated again and again. Prove thatas the number of iterations n of the operation tends to infinity,the concentrations of wine in both containers tend to equal eachother.
