Rules: Fill in the grid so that each row, each column, and each 3 x 3 block contains the integers 1, 2, 3, 4, 5, 6 exactly once and the star symbol * exactly three times, AND so that the set of stars obeys 180 degree rotational symmetry.
Research thoughts: In a way, this week's puzzle is like a normal Sudoku puzzle with the numbers 7, 8, and 9 replaced by stars (and with an additional symmetry condition). Consider the set of all 9 x 9 Sudoku puzzles where the 7, 8, and 9 have been replaced by stars, with or without extra symmetry conditions. Here is an open question: Given that the number of 9 x 9 Sudoku boards is known, how many of these "three star" boards are there? This would be a simple question to answer if the problem of counting normal 9 x 9 boards was solved by first counting the ways to place all the 1's, then all the ways to place the 2's in the remaining spaces, and so on. But alas, that is not how the one known proof of the number of 9 x 9 Sudoku boards happens to work! Perhaps a better proof for counting 9 x 9 Sudoku boards can come from considering k-star puzzles?
Solutions are due by noon on Tuesday, February 14, 2006.
Return solutions ON PAPER to Laura Taalman, Burruss 127, MSC 7803.
Include your name and email address with your solution.