answer:If I understand your question, you can solve the FCG problem without exploring every possible combination. For example, CCCCCCCCCCCC…FGFCF…CCCCC is one possible (incorrect) solution that would only be run by a very poor program. Long before that solution had been tested, you’d have the solution. The answer is rather easy to test as the process requires a finite number of possible steps: 1. If the chicken is left with the grain, it eats the grain 2. If the fox is left with the chicken, it eats the chicken. 3. If the fox is left with the grain, nothing happens. The solution becomes obvious: 1. You take the chicken across and leave it. 2. You take the fox across and pick up the chicken. 3. You take the grain across and leave the chicken. 4. You take the chicken across. See this for more information.