# Interesting

Sudoku is not only a fun puzzle, sudoku also turns out to be very interesting in other ways and in making people think. In my own field, mathematics, for example, there is a lot of interest in sudoku with a lot of questions: How many digits must be given at least to create a uniquely solvable sudoku? How many different sudoku actually exist? And many deeper mathematical questions. In the presentation below, which can also be downloaded via the second link, a number of these aspects are explained:

There are also artists who are inspired by sudoku. Take a look at the work of Henriëtte Wiessing:

Variations on the original sudoku are also constantly being thought up. For example, there is a nice book by Aad Thoen and Aad van de Wetering entitled “Exotische sudoku’s” (in Dutch), with indeed all very exotic sudoku’s, with different rules than we are normally used to. A very nice one is the sudoku below, in which the given numbers are in the form of a circle and represent the decimals of the number π. This is nice, because the number π has everything to do with circles: the circumference of a circle is 2πr and the surface πr^2, if r is the radius.

Annet Hiltermann, landscape painter (http://www.annethiltermann.nl/), has also been involved for many years in the production of very special sudokus. Below her 89th sudoku, which was given the name “Cross sudoku”. If a digit is larger than all of its neighboring digits (in horizontal and vertical directions), it is in a pink box, and if it is smaller than all of its neighboring digits (in horizontal and vertical directions), it is in a blue box. Try to solve the sudoku below, it will take quite some effort! The solution is here.

There are many more variants of the traditional sudoku, all with their own rules. The next one is also very interesting, and here you can find how to solve this sudoku. The extra rules for solving this sudoku are as follows:

- Two squares connected by a horse jump from chess do not contain the same number (horse jump: 2 squares to the left or right, followed by 1 square up or down; or 2 squares up or down, followed by 1 square to the left or right).
- Two squares connected by a king’s move in chess do not contain the same number (the king may walk 1 square in all directions, including oblique).
- Two boxes horizontally or vertically next to each other cannot contain digits that differ by only 1

Here’s the sudoku; the extra requirements mean that we need less than the usual 17 digits at the beginning. In this case 2 digits are sufficient!

The solution of the puzzle can be found here. More of these challenging sudoku’s are discussed on the youtube channel of “Cracking the cryptic”, every day new sudoku’s!