i) Sometimes, solutions have very limited solute-solubility. How could you force such atoms to mix and form a random solution with a solute concentration that is well above the solubility limit?

ii) Atoms of A and B are arranged in a straight line at random, with the mole fraction of B equal to x. What is the probability of finding two A atoms next to each other? How would your calculation be modified if this was a two-dimensional array of A and B atoms?

iii) An alloy is to be made, containing Fe, Mn, Al, Au and Mg. What are the con- centrations of these elements that result in a maximum configurational entropy of mixing?