17
Gary McGuire of University College Dublin shows in a proof posted online on 1 January1 that the minimum number of clues — or starting digits — needed to complete a puzzle is 17; puzzles with 16 or fewer clues do not have a unique solution.
Is there only one answer to a Sudoku puzzle?
The short answer is yes! There is no rule that requires Sudokus to have a unique solution. Sudokus can have multiple solutions or only one unique solution based on the initial starting clues and their positions in the grid.
What is a minimal Sudoku?
A proper puzzle has a unique solution. A minimal puzzle is a proper puzzle from which no clue can be removed without introducing additional solutions. See Glossary of Sudoku for other terminology.
Is there a mathematical solution to Sudoku?
When one hears that no math is required to solve Sudoku, what is really meant is that no arithmetic is required. The puzzle does not depend on the fact that the nine placeholders used are the digits from 1 to 9. In fact, mathematical thinking in the form of logical deduction is very useful in solving Sudokus.
What is a jellyfish in Sudoku?
If a particular candidate is present in four or less Cells in four Rows and if these Cells belong to the same four Columns, then whichever Cells the candidate is the solution for in any of these four Rows, these Cells must be in different columns.
How many minimal-clue Sudoku puzzles are there?
How many minimal-clue sudoku puzzles are there? It is known that there are a minimum of 17 clues needed to create a proper sudoku puzzle. For how many puzzles is 17 sufficient? From the history of the minimal proof, I gather that there are multiple puzzles for which 17 clues are enough for a unique solution.
What makes a Sudoku different from a normal Sudoku?
Ordinary Sudokus (proper puzzles) have a unique solution. A minimal Sudoku is a Sudoku from which no clue can be removed leaving it a proper Sudoku. Different minimal Sudokus can have a different number of clues.
What is the aim of a Sudoku puzzle?
As you probably know, the aim of a Sudoku puzzle is to complete a partially-filled nine-by-nine grid of numbers. There are some guidelines: the numbers one to nine must appear exactly once each in every row, column and three-by-three sub-grid.
How many possible solutions are there to the Sudoku problem?
There are exactly 6, 670, 903, 752, 021, 072, 936, 960 possible solutions to Sudoku (about 10^21) . That’s far more than can be checked in a reasonable period of time. But as luck would have it, it’s not necessary to check them all.
