Numbo - pgs 127- 138

Daniel Defays, during his sabbatical year at Ann Arbor with Douglas Hofstadter in the late eighties, designed and implemented a puzzle-playing program based off of ideas about human problem solving. His game "Le Compte Est Bon" ("the total is correct") is generalized as follows: there are five randomly chosen integers and one larger integer, the goal is to use addition/subtraction/multiplication to make the five equal to the one.

It is trivial to enumerate all of the possible answers using a computer program to model the "Numble" world. But how to do it with goals of discovering how the human mind works on these problems?

Defays architecture utilizes the rote learning of arithmetic tables we are all subjected to memorizing in grade school. He considers these to be part of a larger system which teases apart the problem in our brain. I like to think of it as a form of preprocessing. When the program first encounters a problem, it may try to use a top-down approach -- starting with the goal and then compiling clusters of numbers and operations which fall within range of the goal. Beyond the arithmetic tables of 0-12, there are also some "landmark" numbers which appear to have special appeal to us humans -- digits of 2, 5, 10, exponential numbers, etc. These can be exploited to get within range of similar numbers. The book uses the example of getting in range of 146 by noting that 144 = 12 x 12, this is a reasonable starting place for problem solving.