Sudoku 4B

My image “Sudoku 4B” was chosen for the American Mathematical Society 2012 Mathematical Imagery calendar (see the 2011 calendar here. Yay! The image is based on the puzzle. In standard Sudoku, a 9 × 9 grid is partially filled with numbers 1 – 9. The objective is to complete the grid, placing a single-digit number into each unfilled square, such that:
• each number 1 – 9 appears once and only once in each row,
• each number appears once and only once in each column, and
• each number appears once and only once in each of the 3 × 3 smaller squares (shown outlined by a thick line below).
The first grid shows an example puzzle, with its solution in the second grid.  Although the puzzle is generally given with numbers, there’s nothing particularly numeric about Sudoku—it’s about patterns of figures. Letters or other symbols can be used, or, in my case, shapes. Also, a simpler puzzle can be obtained by using a smaller grid, say a 4 × 4. This next grid shows a 4 × 4 Sudoku, using the numbers 1 – 4. Mapping the numbers to four different (but similar) shapes gives this grid: For my image, I did this four times, using four different basic shapes:  and then combined them by adding all four together.

Next stop, a full 9 × 9 Sudoku!