And let the free market sort it out. Or is it impossible to wean the self-sufficient capitalists from free government services?

It looks like the board has the equation X = G/(CHROM - 3). Each of the variables is defined on the blackboard. So it's just simple calculus to get the numerical values. The url just came from the numerical answer, where the numerator references goo.gl, and the denominator gave the shortened url in letters represented as pairs of numbers (a=1 b=2...) The bit about Chromium and Uranium was interesting, as it gave meaning to what X meant, but it wasn't important to finding the prize.

Actually, negative temperatures can exist, if you work with the thermodynamic definition of temperature. If the entropy of a system decreases as its energy increases, then it has negative temperature. For example, a system with 2-state paramagnets has maximum entropy when there is no magnetic field being applied. As a field is applied, the paramagnets tend to absorb energy and align with the field, which means the system's entropy decreases. And thus we have a negative temperature.