Problem of the Week 1100

Naked Sudoku

Solution

Problem 1100 was solved by several of you, and by Macalester students Kat Edwards, Casey Battaglino, and David Dembinski. One correspondent thought there was no solution -- this often happens when one makes a mistake in a Sudoku.

Carl Libis observes that one can start as follows:

It is clear that the digits '9' will go only in pink squares. Since column 8 only has one pink square, a '9' must go in that position -- row 6-column 8, or the (6,8) position. This now leaves only the pink square in column 9 available, so a '9' must go in the (9,9) position. Now column 7 only has one pink square available for a '9,' so a '9' must go in the (1,7) position. Now there is only one pink square in the 2nd, 3rd, 5th, and 8th row, so a '9' must go in the (2,3) position, the (3,6) position, the (5,2) position, and the (8,5) position. Only positions (4,4) and (7,1) are left for a '9.' Similar reasoning finishes it off; details omitted.

The fully dressed sudoku:

An unresolved point is: What is the most naked Sudoku you can get? By this I mean: Can one delete some of the inequalities in Problem 1100 and still have a viable puzzle, with a unique solution? Presumably so. One could just carefully go through the logic of the solution and note which inequalities were used. But if one posed the puzzle with just those inequalities, would that make it easier or harder? There is less information, but that also might be a guide to finding the solution!

[Back to Problem 1100]

© Copyright 2008 Stan Wagon. Reproduced with permission.