Problem of the Week #4
Spring 2006:
Special All-Sudoku Semester
This week's puzzle is a normal Sudoku puzzle with four additional regions.
Sudoku puzzles with additional regions are not uncommon; probably the most
popular variant of this type is "Sudoku X", where each of the main diagonals
is also required to be a Sudoku region. (We will call something a "Sudoku
region" if it is a region that contains each of the characters in the
puzzle exactly once.) In this puzzle we have four extra pyramid-shaped
Sudoku regions.
Rules: Fill in the grid below so that each row, each column, each 3x3
block, AND each of the shaded pyramid regions contains each of the numbers
1, 2, 3, 4, 5, 6, 7, 8, and 9 exactly once.
A laundry list of questions to ponder (some are known and some are not):
Not every connected region of 9 squares can be a Sudoku region; can
you find one that can not be?
How many different connected 9-square regions can be
valid Sudoku regions? What about non-connected regions?
What percentage of 9 x 9 Sudoku boards have the
"four pyramids" property of this week's puzzle?
Can you find a board with
extra Sudoku regions, each of which are "legal" on their own, but so that
the board has no solution (i.e. the extra regions are too restrictive when
taken all together)?
Solutions are due by noon on Tuesday, February 7, 2006.
Return solutions ON PAPER to Laura Taalman, Burruss 127, MSC 7803.
Include your name and email address with your solution.