We study the problem of finding two solutions to a constraint satisfaction problem which differ on the assignment of as many variables as possible – the Max Hamming Distance problem for CSPs – a problem which can, among other things, be seen as a domain independent way of quantifying “ignorance.” The first algorithm we present is an $\mathcal{O}(1.7338^n)$ microstructure based algorithm for Max Hamming Distance 2-SAT, improving the previously best known algorithm for this problem, which has a running time of $\mathcal{O}(1.8409^n)$. We also give algorithms based on enumeration techniques for solving both Max Hamming Distancel-SAT, and the general Max Hamming Distance (d,l)-CSP, the first non-trivial algorithms for these problems. The main results here are that if we can solve l-SAT in $\mathcal{O}(a^n)$ and (d,l)-CSP in $\mathcal{O}(b^n)$, then the corresponding Max Hamming problems can be solved in $\mathcal{O}((2a)^n)$ and $\mathcal{O}(b^n(1+b)^n)$, respectively.