$$(9\times 1)+(9\times 2)+\cdots+(9\times 9)=9\times(1+2+\cdots+9)=9\times 45=405$$Īnd each entry is in exactly one row, one column, and one region, so each entry is counted three times when forming the sum of the rows, columns, and regions, so that the sum is $3\times 405=1215$. To see this, just note that the sum of the entries is There actually is a way, using only arithmetic, to check whether a sequence of nine numbers each between $1$ and $9$ contains all unique elements: for each number $n$ in the sequence, replace it with $2^$'s, regardless of whether they form a correct Sudoku board. that there is not an arithmetic way to check for set uniqueness? I am ready to be shown the err of my ways, but it would be cool to confirm that a board can be solved without confirmation that each cell value is valid. This has me thinking I am overlooking something with my math and logic, but I can't think of a board where the sum of the sets wouldn't be 1215 or a board where the sum would be 1215 and it would be an invalid board.
If youre just starting out, selecting 'pencilmarks' and/or 'validity' might make things easier, and if you. Click on each cell with your mouse and enter a number from 1 to 9 using your keyboard. Every row, column, and 3 x 3 box should contain one of each digit.
#Sum sudoku online free#
All math and logic seem dedicated to solving puzzles (as in finding the correct digit for each cell) or to generating solvable puzzles. Play Free Sudoku Now Sudoku is one of the most popular puzzle games of all time. Digits from 1 to 9 are placed in each empty cell. If the assumption above is correct, is this sum unique to solved puzzles, or are there permutations of a completed (but not solved) board that would give 1215 using the same method?Īfter a general search and skimming 2 wikipedia articles on Sudoku mechanics (Mathematics of Sudoku and Sudoku Algorithms), I'm still not seeing this simple approach to verifying a board as solved. This is based on taking the sum of each digit in the set (1+9 + 8+2 + 7+3 + 4+6 + 5 = 45) and multiplying by the total number of sets (9 rows + 9 columns + 9 quadrants = 27), so 45 * 27 = 1215. Digits are strictly increasing from the round bulb of the thermometer to each flat end. Some thermometer shapes are placed in the grid.
Proof that are the inverse is true, that all Y's are X, or, if it's not true, example of X that is outside the Y set.Īll solved Sudoku puzzles, where "solved" is defined as a 9x9 grid having the set 1-9 in each column, row, and 3x3 quadrant, can be verified as solved by taking the sum of each row, column, and quadrant, as the sum will always be 1215. I have been solving and making Killer Sudoku puzzles since 2005 and although my Sudoku solver has been part of this site. Place a digit from 1 to 9 into each of the empty squares so that each digit appears exactly once in each of the rows, columns and the nine outlined 3x3 regions. Each term in the summation is the sum of.
#Sum sudoku online verification#
Verification that my math is correct for the assumption that all Xs are Y. For n×n Sudoku puzzles with square blocks, Stirling's formula may be used to show that each binomial.
Fundamentally, I'm looking for help on two things:
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