My MAT 381 presentation on Wednesday October 12 is on using elements of number theory in order to solve the newspaper puzzle Kenken and to make it a bit more challenging.

KenKen is a puzzle that appears in daily newspapers the world over and is similar to Sudoku. In KenKen, you need to solve an nxn grid using the integers 1 through n, making sure not to repeat them in a given row or column. Where it really differentiates itself from Sudoku is that it uses the basic arithmetic operations on a given integer in a given group of squares. In order to solve the puzzle, you need to abide by the operations in a group of squares that are littered throughout the puzzle, while simultaneously avoiding repetition.

Number theory gives us a few tools that can help us solve a KenKen puzzle or make it more fun for a math major. Of note are triangular numbers and Gaussian integers.

Triangular numbers are numbers that can be represented in the form of a triangle composed of equally spaced points where the 1st row has one point and each subsequent row has one more element than last. The sum of the points is the resulting triangular number.

A Gaussian integer is a complex number a+bi where a,b are integers and i is, of course, the square root of -1.

With that, I look forward to setting the bar real low for the rest of the semester on Wednesday. See you then.

Kyle

It was a nice talk. You demonstrated the use of number theory and logic in solving the game, and gave a good example of a variation of the game using arithmetic in the strange ring of Gaussian integers. Please include a reference to the paper that inspired your talk.

The article, which can be found in JSTOR:

Triangular Numbers, Gaussian Integers, and KenKen

John Watkins

The College Mathematics Journal

Vol. 43, No. 1 (January 2012), pp. 37-42