Killer sudoku combinations

Killer sudoku also killer su dokusumdokusum dokukiller sudoku combinations, sumokuaddokuor samunamupure is a puzzle that combines elements of sudoku and kakuro. Despite the name, the simpler killer sudokus can be easier to solve than regular sudokus, depending on the solver's skill at mental arithmetic ; the hardest ones, however, can take hours to solve. A typical problem is shown on the right, using colors to define the groups of cells. More often, puzzles are printed in black and white, with thin dotted lines used to outline the "cages" see below for killer sudoku combinations.

Killer Sudoku adds a new dimension to standard Sudoku, requiring arithmetic to solve. You will need new specialised Killer Sudoku solving techniques to progress in these puzzles besides the standard Sudoku techniques you will already know. An essential Killer Sudoku solving technique is the "45 rule". This uses the fact that every row, column and block must contain each of the numbers 1 to 9 once. Therefore, the total of all numbers in one row, column or block will always be Take the first column of the Killer Sudoku shown in Figure 1.

Killer sudoku combinations

Remembering common unique combinations is essential if you want to improve your time for solving killer sudoku puzzles. As well as cell cage combinations, we've included required digits further down. Some cells always require particular digits, regardless of the number combination that goes into them. Knowing these is a great way to eliminate candidate numbers from blocks, rows, and columns. Is it cheating? We call it a cheat sheet, but is it really cheating? Only you can decide! Our view is that a reference like this is no more cheating than using a dictionary to check your spelling. For us, puzzles like killer sudoku are all about the logic and not an exercise in memory or recall. New to killer sudoku? Be sure to check out our Killer Sudoku From Scratch tutorial. Love logic puzzles?

Even though the vast majority of killer sudoku puzzles followed the rule anyway, English-speaking solvers were confused about appropriate solving strategies given the ambiguity.

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Killer Sudoku is a variation that adds additional sub-regions of 2 or more cells with a number in the corner of each sub-region. The numbers placed in the cells of the sub-region must be unique in that sub-region even it the sub-region spans more than one row, column or region and must add up to the number in the corner of the sub-region. Sub-regions are shown by dotted lines which group cells together. You can use all the standard Sudoku Solving Techniques with Killer Sudoku, but there are several techniques specific to the addition of the sub-regions. The Rule of 45 is a key technique that can be extended to multiples of 45, along with Combination Elimination. These are explained below. The Rule of 45 can lead you to some simple placements as you begin to solve. If all sub-regions but one are fully contained in a row, column or region inside cells its possible to work out the value of the remaining cells outside cells.

Killer sudoku combinations

A Killer Sudoku contains cages and cage sums. Knowing the number of cells in a cage and its sum, we can determine the possible cage combinations , i. For example, if we have a cage of 2 cells whose sum is 5, written 15[2], then either it contains the digits 1 and 4, or the digits 2 and 3. Manually enumerating the cage combinations for arbitrary cages can be very tedious, but some helper programs such as SumoCue can automatically compute the cage combinations for the player. However, for some cages, the cage combinations are easy to enumerate and can lead to candidate eliminations , either simply because the candidate is not part of any combination, or in conjunction with some other technique. One should be careful to list all combinations. Then we can eliminate the digits 1 to 6 from all three cells in the cage. Further, if all the three cells all belong to the same line or nonet , we can then apply Naked Triple to that line or nonet. Either way, the cage must contain the digits 8 and 9 in 2 of the 4 cells.

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Remembering common unique combinations is essential if you want to improve your time for solving killer sudoku puzzles. Only you can decide! The 14 cage can now be completed by solving the other square as a 9. A short-cut to calculating or checking the value of a single 'innie' or 'outie' on a large number of cages is to add up the cages using 'clock' arithmetic formally, Modular Arithmetic modulo 10 , in which all digits other than the last in any number are ignored. This article needs additional citations for verification. Read Edit View history. Killer Sudoku adds a new dimension to standard Sudoku, requiring arithmetic to solve. Puzzle Genius is an imprint of Shelfless. For us, puzzles like killer sudoku are all about the logic and not an exercise in memory or recall. Looking at the nonet on the left hand side in the middle, we can see that there are three cages which do not cross over into another nonet; these add up to 33, meaning that the sum of the remaining two cells must be Knowing these is a great way to eliminate candidate numbers from blocks, rows, and columns. When two numbers are added together, the last digit of the total is not affected by anything other than the last digits of the two original numbers. For example: a 4 cell cage totaling 13 has the possible combinations of 1, 2, 3, 7 , 1, 2, 4, 6 , or 1, 3, 4, 5.

If you've struggled to complete tricky, tough, or deadly Killer Sudoku puzzles then this App could be for you. The results are clearly displayed with any duplicate numbers highlighted in red. The target number of cells and their sum is entered using the edit tool.

Example: A set of cages form a complete nonet with an 'outie'. Be sure to check out Puzzle Weekly — our free weekly collection, delivered to your inbox every Monday. Traditionally, as with regular sudoku puzzles, the grid layout is symmetrical around a diagonal, horizontal or vertical axis, or a quarter or half turn about the centre. By convention in Japan, killer sudoku cages do not include duplicate numbers. Adding together a number ending in 7 and a number ending in 8 always results in a number ending in 5, for example. Even though the vast majority of killer sudoku puzzles followed the rule anyway, English-speaking solvers were confused about appropriate solving strategies given the ambiguity. Category : Sudoku. An essential Killer Sudoku solving technique is the "45 rule". For example: a 4 cell cage totaling 13 has the possible combinations of 1, 2, 3, 7 , 1, 2, 4, 6 , or 1, 3, 4, 5. This article includes a list of general references , but it lacks sufficient corresponding inline citations. Please help improve it or discuss these issues on the talk page. Arithmetical puzzle game. Clock arithmetic should at most be used with caution for houses with more than one 'innie' or 'outie', when more than one set of values may result in the same final number, but may still be useful as a quick arithmetic check. Read Edit View history.