Nimble Numbo

Nimble, Numbo: numbers mumble [like letters in Jumble] their little hints to bursting brains, “try me, I’ll take you to the target” and cross-ey'd we decrypt, accordingly. 

Hoffstadter describes in "Numbo: A Study of Cognition and Recognition" the Numbo program. Here's an analogy: Jumbo is to letters and Numbo is to ______.  [The answer is "numbers"]

Hoffstadter describes how the context of a specific target number can  change the salience of a brick-number (the numbers used, along with the four basic artithmetic opperators, to reach the target). The 8 and 10 become more salient when the target is 87, as does the 7. According to DH the rapidity of solutions is determined by two types of information: a priori knowledge and syntax. Types of knowledge come into play, but as I found when trying this type of crypto problem some solutions came more intuitively. Specifically, when no answer is immediately obvious my first searches are more likely to involve addition or subtraction. 

Right now it seems pretty likely that we will be programming a Numbo like program to solve crypto problems in a human-like way. If this program were modeling my brain, I'd probably have it try some addition and subtraction combinations after assessing the approximate size of numbers (a type of knowledge Hoffstadter describes is used in playing Numble). Small arithmetic would be rote, some would be procedural knowledge. I imagine in deciding which would be rote and which would not be, I would use my own rote knowledge. 12 x 12 is rote, 12 x 13 is not, 9 x 5 is, etc.