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How do you fairly allocate different sized rooms in rental housing for students with different sized budgets?

Abbreviated Question: 
How do you fairly allocate different sized rooms in rental housing for students with different sized budgets?
Answer: 

Roughly speaking, you need to compute the aggregate valuation of the students for each house.  They should then rent the house for which the gap between their aggregate valuation and the house’s rent is the largest.  They can then allocate the surplus (valuation minus rent) among themselves in some way – for instance, divide it equally.  So, for instance, if the valuation of student i for the room she ends up getting is B_i, and the total rent is R, then the aggregate valuation is V=B_1+...+B_5.  The surplus is then V-R.  Each student gets (V-R)/5, so the rent stude