When reading through the material this week, I encountered a lot of problems I’d never been asked before. Naturally I attempted to solve them myself before looking up the answer (as I’m sure most people did), and some of the problems proved to be more difficult than others. One of the problems that stood out to me, however, was Luchins water jug problem.

               A family favorite movie growing up was Lethal Weapon. At one point in the movie, the terrorist asks Danny Glover and Mel Gibson to solve a water jug problem of their own. They are provided with a 3-gallon jug, a 5-gallon jug, a computer to weigh the final product, and are told they must come up with exactly 4 gallons of water or a bomb will explode. They tell you how to solve the problem in the movie, but every once in a while, I find myself remembering this problem (like I did today) and trying to remember how to solve it (say if I found myself trying to diffuse a bomb).

According to our reading this week, I see my problem in terms of an initial state, the condition at the beginning of the problem, and a goal state, the solution of the problem (Goldstein p. 341). The initial state is the two empty jugs, and the goal state will be one of the jugs filled with exactly 4 gallons of water. I then use operators, actions that take a problem from one stage to the next (Goldstein p. 341) to move from the initial to goal state. At first, I have trouble solving the problem due to my mental set, or the preconceived notion about how to approach a problem (Goldstein p. 340). I know that one jug can only hold 3 gallons of water and that the other is supposed to hold 5, so how do I get to exactly 4?

Using means-end analysis, a strategy designed to reduce the difference between the initial and state goals (Goldstein p. 343), I’ll create my subgoals, intermediate steps between the initial and end state, to break the problem down as simply and succinctly as possible. My initial state, goal state and subgoals are all housed in my problem space (Goldstein p. 343), and the problem ends up looking something like this: I fill up the 3-gallon jug and dump it into the 5-gallon jug. Then I fill up the 3-gallon jug again, and dump 2 of the 3 gallons into the 5-gallon jug (only 2 will fit since there was already 3 gallons). This leaves me with 1 gallon in the 3-gallon jug, and 5 gallons in the 5-gallon jug. I empty the 5-gallon jug, dump the 1 gallon from the 3-gallon jug into the 5-gallon jug, refill the 3-gallon jug and dump those 3 gallons into the 5-gallon jug holding 1 gallon of water, and end up with exactly 4 gallons!

While I was able to easily list out the steps in this blog post, my problem space was a little less clear. It always takes a second for me to figure out the math behind the problem, and I’ve normally wandered down a few different paths by then. I can’t imagine how things would go if I had to do the “talk out loud” task!

Reference:

Goldstein, E. Bruce (2017). Cognitive Psychology: Connecting Mind, Research, and Everyday Experience. Stamford, CT: Cengage Learning.