In both the top row and the left-most column. In the example shown on the right, the location of the number 1 is already known (even if its exact location is still unknown), no other block may have that same number in the In this next technique, we useĪssigned to a given row or column of a specific block Only one remains in a cell, so then we know that cell's value. Once all the singles have been found, I usually start marking. Then it is also not possible anywhere else in the same row/column. Then it is also not possible anywhere else in the same block.Īnd it is not possible anywhere else in the same block, ![]() When a candidate is possible in a certain block and row/column,Īnd it is not possible anywhere else in the same row/column, Row/Column Range Checking ("locked" candidates) examples This idea is more fully discussed mathematically in The 12 Rules of Sudoku. If a candidate k is possible in the intersection of A and B but not possible elsewhere in A, then it is also not possible elsewhere in B. Using "A" and "B" here for some number of rows, columns, cells, or blocks, then we have: Most people do this step without actually making any marks.įirst of all, if the rules discussed below sound pretty much the same, it's because they are all just permutations of the same Cross-hatch scanning is generally all that is necessary for "easy" puzzles. This process, referred to as cross-hatching, is repeated for each row and each column. "hidden" by the presence of the other marks. The 5 in this cell is called a "hidden single" because it can only be in this single location, and that fact is Since a number can only appear once in any given column or row and must appear exactly once inĪny given 3x3 block, the easiest place to start is to first checkįor cells that must hold a value because no other cell in a 3x3 block can hold that number.įor example, in this case the number 5 is excluded from all but one cell in the top center 3x3 block. But in that top middle block only one cell can hold a 5. In that cell the numbers 4, 5, 6, and 8 are all possible. The dots in the cell in row 3, column 5, indicate that You should always start a Sudoku by finding all the hidden singles. Despite the name, hidden singles are far easier to find than naked singles. There is only one possible cell for a candidate. There is only one possible candidate for a cell a hidden single arises when This situation can arise for one of two reasons. When a candidate k is possible in only a single cell ofĪ row, column, or block, then that cell must be k. Hypothesis and proof and a sort of depth.Īll of these techniques are based on identifying all the possible "candidates" for a cell (indicated by marks)Īnd then eliminating them one by one until only one possibility remains in a given cell.Ĭross-Hatch Scanning (looking for singles) When all that fails, the Sudoku Assistant resorts to Almost-locked set analysis can be extended to grids, where itĪnd also to what I am calling almost-locked ranges. What I'm calling 3D Medusa analysis, includingĪnalysis. Addendumįor a more efficient program for solving Sudoku puzzles, with an interesting discussion of the approach, see Peter Norvig's Solving Every Sudoku Puzzle.The Sudoku Assistant uses several techniques to solve a Sudoku puzzle: Here's the whole Sudoku program in a single file: Sudoku solver program. ![]() On an ATSAMD51-based board such as the Adafruit PyBadge the "world's hardest Sudoku" takes approximately 128 seconds to solve. The program prints out the solution for example here's the solution to a different Sudoku, in case you want to try solving the "world's hardest Sudoku" by hand before running the program. (format t "Sorry, solution not found."))) To run the program call (solve): (defun solve () The guess routine calls check to check that the number is the current cell obeys the Sudoku rules: (defun check (num row col)įinally, print-board uses format statements to print the solution in a readable layout: (defun print-board () ((plusp (aref board row col)) (guess (1+ index))) Note that the program fills in the array as it solves the Sudoku, so if you want to run it again you need to reinitialise the array. This is one designed by Dr Arto Inkala of Finland, said to be the hardest Sudoku in the world! (defvar board Descriptionįirst you define the problem, using 0 for empty cells. Note that this example won't run on ESP32 boards because they don't have enough stack space. It will run on the Adafruit ARM M4 boards or the RISC-V boards. It is based on a program by Daniele Mazzocchio. This Sudoku solver demonstrates the new array and format features in uLisp Version 3.2.
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