With the increasing use of the internet, many problem-solving tasks such as resource allocation, scheduling, planning, and configuration pose themselves in an open setting involving multiple participants. Existing search-based problem-solving techniques are based on the closed-world assumption and require that all options be collected before problem-solving can start. This approach of turning the web into a virtual database often leads to gathering much more information than necessary to solve the problem. We consider constraint satisfaction as the most successful practical problem solving technique, and define open constraint satisfaction where values are incrementally gathered during problem solving. We present several algorithms for open constraint satisfaction and show that on random problems, they require gathering significantly less values. We then extend the technique to constraint optimization using the fuzzy CSP model, and show that here too great efficiency gains can be achieved by coupling problem solving and information gathering.