Other problems involve making a series of changes to achieve a specific goal, a process called transformation.
Example: A familiar riddle describes a situation in which a man has to take his fox, his chicken, and his tub of grain across a river in a boat. The boat will hold only him and two of his possessions at any one time. He can’t leave the fox and the chicken on the riverbank by themselves because the fox will eat the chicken, and he can’t leave the chicken with the grain because the chicken will eat the grain. He also can’t take the fox and the chicken in the boat together because the fox will eat the chicken when he’s occupied with rowing the boat. The same goes for the chicken and the grain. How will he get all three across? First he takes the fox and the grain across. He leaves the fox on the opposite bank and takes the grain back with him. He then leaves the grain on the bank and takes the chicken across. He leaves the chicken on the opposite bank and takes the fox back with him to retrieve the grain.
There are many strategies for solving problems, included trial and error, algorithms, deductive reasoning, inductive reasoning, heuristics, dialectical reasoning, forming subgoals, using similar problems, and changing the way the problem is represented.
Trial and error involves trying out different solutions until one works. This type of strategy is practical only when the number of possible solutions is relatively small.
Example: It’s dark, and a man is trying to figure out which button on the dashboard of his newly rented car switches on the headlights. He might press all the available buttons until he finds the right one.
Algorithms are step-by-step procedures that are guaranteed to achieve a particular goal.