Clueless Sudoku

Same rules of the standard sudoku, i.e., fill the digits 1 through 6 into the grid so that no digit repeats in any row, column, or bold region. In addition, the sum of the digits in every bold region must be the same.

 
 
Clueless Sudoku Puzzle
 
 

There are 14 bold regions (also called blocks) as can be identified by the different colors in the figure and also defined below.

  • 1: [(1, 1), (1, 2), (1, 3), (2, 1)],

    2: [(1, 4), (1, 5), (2, 5)],

    3: [(1, 6), (2, 6)],

    4: [(2, 2), (2, 3)],

    5: [(2, 4), (3, 4)],

    6: [(3, 1), (4, 1)],

    7: [(3, 2), (3, 3), (4, 3)],

    8: [(3, 5), (3, 6), (4, 5)],

    9: [(5, 1), (5, 2), (4, 2)],

    10: [(4, 4), (5, 4)],

    11: [(5, 5), (5, 6), (4, 6)],

    12: [(6, 1), (6, 2)],

    13: [(5, 3), (6, 3)],

    14: [(6, 4), (6, 5), (6, 6)]

Source: Adapted from the book The Opex Analytics Weekly Puzzle

 
Answer
Analytics Solution
 

Diving Deeper

  • Traditional sudoku can be challenging but at least it comes with some numbers already placed in the grid that can help you to get started.

    The Clueless Sudoku is mean! It doesn’t give you any hint to start with. It doesn’t even tell you what the sum of the digits in each region should be. However, you may be able to figure that out with a little bit of math.

  • Suppose there are 6 nurses that serve a hospital. Nurse N6 has the most experience and can serve 6 patients per shift. Nurses N5, N4, N3, N2, and N1 can serve 5, 4, 3, 2, and 1 patient per shift, respectively. In every shift, the number of patients to be served is the same, and the number of nurses that can work on each shift is pre-defined. Each nurse can serve six different divisions of the hospital. And each nurse can serve six different categories of patients. No nurse can serve more than one division within the same category. And no nurse can serve more than one category within the same division. How can we assign nurses to shifts?

    This is the same problem as the Clueless Sudoku. Don't see how? Nurses are digits, rows are divisions, columns are categories, and regions are shifts.

    All right, maybe there is no such problem in a real hospital setting. But there are variations of this for sure.

  • Sudoku is one of the puzzles most used to illustrate the use of mathematical optimization and constraint programming.

    Mathematical optimization might not sound like a sensible option because there is no objective to optimize in the Sudoku problem. However, optimization solvers for mix-integer programming (MIP) are incredibly good at finding feasible solutions for highly constrained problems, because this is part of their job of finding the best solution whenever there is an objective to minimize or maximize.

 
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