The Kenerator

Automatic Puzzle Producer

Mr. Miyamoto is a totally nice guy. But, as KENKEN grew, he was slightly hesitant to keep creating millions of new puzzles by hand, every day of the year, all by himself. (It would definitely cut into his scuba-diving time.) So the Kenerator was born: a complex artificial-intelligence computer program that generates and checks every new puzzle. The Kenerator was designed with the oversight and according to the specifications of Mr. Miyamoto, working side-by-side with leading artificial-intelligence expert David Levy.

When we run the Kenerator software we first set it according to various criteria, for example:

1. The target difficulty level;
2. How many "freebies" (single square cages) we want in the puzzle;
3. Which arithmetic operations we want to be used in the puzzle;
4. Which digits we want to be used in the puzzle (for example a 6x6 puzzle normally uses the digits 1-6 but we could, if we wished, specify it to be a different set of the digits taken from the whole range 1-9.
5. Whether or not to show the arithmetic symbols in the puzzle (we can make the puzzles harder by omitting these symbols).

Then the Kenerator instantly verifies that each “cage” is correct, that no number appears more than once in a row or column, and most importantly, that each KENKEN puzzle has only one solution.

There is a module in the software, which pretends that it is a user and attempts to solve the puzzle. This module assesses the actual level of difficulty: easiest, easy, medium, or hard, employing a personalized algorithm based on a wide variety of factors. If the actual level of difficulty is as required, i.e. it conforms to the target set at the start of the Keneration process, then the puzzle goes into the "accepted" pile, otherwise it is rejected and the Keneration process starts over again.

And you thought we just picked the numbers out of a hat, didn’t you?