1. A system for solving a constraint satisfaction problem (CSP), the system comprising: one or more processors coupled to memory for executing one or more instructions in a computing environment; a logic unit for identifying a first illegal combination associated with at least one variable, wherein the first illegal combination contradicts at least one constraint; a logic unit for grouping the first illegal combination with a second illegal combination, in response to determining that the first and second illegal combinations contradict the same constraint; a logic unit for identifying at least one failure explanation for each group of illegal combinations, wherein the failure explanation is associated with at least one illegal combination in said group to provide a reason for a contradicted constraint associated with the illegal combination; a logic unit for assigning a value to each variable in the given domain to solve the CSP within the limitations defined by the constraints in a solution path; a logic unit for generating a first result, in response to determining that the assigned value to each variable satisfies the constraints; and a logic unit for generating a second result, in response to determining that at least one assigned value to a variable contradicts a constraint, wherein the second result includes a context-based explanation for the reason why the contradiction between the assigned value to the variable and the constraint exists, wherein the context-based explanation is based on input to the system by a human operator with specific knowledge of groups of illegal combinations, wherein such context-based explanation is not otherwise known or determinable by a human operator who lacks the specific knowledge, and wherein a plurality of human operators with specific knowledge of various groups of illegal combinations input context-based explanations to the system for various groups of illegal combinations to help a person without such specific knowledge easily understand the reason for the generated results.