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 microstructure based algorithm for Max Hamming Distance 2-SAT, improving the previously best known algorithm for this problem, which has a running time of . We also give algorithms based on enumeration techniques for solving both Max Hamming Distance l-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 and (d,l)-CSP in , then the corresponding Max Hamming problems can be solved in and , respectively.