Thinking Problem Solving Cognition

Given water jars of size 21, 127, and 3 units and an unlimited supply of water, how can you obtain exactly 100 units of water?" This is a well-defined problem because the given state is clearly specified (you have empty jars of size 21, 127, and 3), the goal state is clearly specified (you want to get 100 units of water in one of the jars), and the allowable operators are clearly specified (you can fill and pour according to specific procedures).

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Problem representation can be broken down further into problem translation, in which the problem solver translates each sentence (or picture) into an internal mental representation, and problem integration, in which the problem solver integrates the information into a coherent mental representation of the problem (i.e., a mental model of the situation described in the problem).

Problem solution can be broken down further into solution planning, in which the problem solver devises a plan for how to solve the problem, and solution execution, in which the problem solver carries out the plan by engaging in solution behaviors.

This is two cents less per stick than butter at Vons.

If you need to buy 4 sticks of butter, how much will you pay at Vons?

It takes sixty days for the lake to be completely covered with water lilies. " In this problem, the problem solver must invent a solution method based on working backwards from the last day.

Based on this method, the problem solver can ask what the lake would look like on the day before the last day, and conclude that the lake is half covered on the fifty-ninth day. It is also customary to distinguish between well-defined and ill-defined problems.

Well-defined problems may be either routine or nonroutine; if you do not have previous experience with water jar problems, then finding the solution (i.e., fill the 127, pour out 21 once, and pour out 3 twice) is a nonroutine problem.

In an ill-defined problem, the given state, goal state, and/or operations are not clearly specified.

Ill-defined problems can be routine or nonroutine; if one has extensive experience in writing then writing a short essay like this one is a routine problem.

The process of problem solving can be broken down into two major phases: problem representation, in which the problem solver builds a coherent mental representation of the problem, and problem solution, in which the problem solver devises and carries out a solution plan.