we turn coffee into puzzles

Puzzles for Chartier article These seven puzzles appeared in the mathematical research article An Integer Programming Model for the Sudoku Problem (Bartlett, Chartier, Langville, Rankin) in the Journal of Online Mathematics, December 2007.

Classic Sudoku The numbers 1--9 must each appear exactly once in each row, column, and block.

Sudoku X The numbers 1--9 must each appear exactly once in each row, column, block, and main diagonal.

Four Squares The numbers 1--9 must each appear exactly once in each row, column, block, and shaded square region.

Pyramids The numbers 1--9 must each appear exactly once in each row, column, block, and pyramid.

Magic Squares The numbers 1--9 must each appear exactly once in each row, column, and block. In addition, each of the shaded squares is a (semi)-magic square, meaning that the minirows and minicolumns of each shaded square sum to the same amount.

Positions The numbers 1--9 must each appear exactly once in each row, column, block, and shaded region. Notice that the shaded regions are not connected; for example, the red region consists of all nine of the red cells in the puzzle.

Greater Than Each of the numbers 1-9 must each appear exactly once in each row, column, and block. In addition, adjacent cells must obey any 'greater than' (>) or 'less than' (<) symbol that appears on their dividing line. Note that this puzzle has no starting clues given; the greater than symbols are enough to determine a unique solution without any initial conditions at all! As an aid in solving, some cells have been shaded. Cells with a lower value than all their neighbors are blue; cells with a higher value than all their neighbors are red.