Lone square An empty square that has all its neighbouring squares either column or row filled in can easily be solved. Simply add together the corrsponding neighbouring values and then subtract the total from the clue. The remaining value is the answer for that square. Any values which appear in the combinations for both runs are candidates for the square on which the runs intersect. However, the only common number in both sets of combinations is 3, therefore the intersection square must be 3. Combo reference This technique works by picking a run and performing a cross reference on every square along it, weening out combinations until you have only 1 left.

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Tips and tricks: easy ways to solve Kakuro A simple puzzle Here is a Kakuro puzzle which will turn out to be very simple to solve.

We give every column a name: the first one is A, the second, B, and so on to the tenth, J. To each row we also give a name: the top row is a, the next, b, and so on to the bottom row, which is called j. Each square lies in the intersection of a row and a column, so we can name it uniquely by giving both the row and column names. For example, the bottom right square is called Jj. In trying to solve a puzzle we will need to have a name for the unknown number that goes into a square.

So, for example, when I need to talk about the number that goes into the square Jj I will write [Jj]. Similarly for any square, when you see square brackets around the name of a square, it means the number that goes into that square. A final convention before we move on to solving the puzzle above. The left-most clue in row c involves breaking 7 into 3 parts. The left-most clue in row j involves breaking 7 into 2 parts.

We will distinguish these by a subscript on the clue: 73 for the clue in row c and 72 for the other. The number is the clue, and the subscript is the number of pieces it should be broken into. Divide and conquer Now let us work up a strategy for splitting a puzzle into smaller pieces, because smaller puzzles are easier to solve. Take the squares Bb, Bc, Cb and Cc. But when the same four numbers are summed row-wise, then the result has to be the same. The sum in the row b has to be 17, because it must match the clue.

This forces the number in [Dc] to be 1. We have converted partial knowledge about four squares into full knowledge of one square. We have divided. Next we will conquer. But first we will state the rule. The rule of divide and conquer When a block of squares is connected to the rest of the puzzle through exactly one square, then call this the linking square. The value in the linking square is found as follows: If the linking square is part of a row clue Find the sum of all the column clues this was 23 in the example above.

Next find the sum of all the row clues except the one that involves the linking square this was 17 in the example. Subtract this partial sum from the sum of the column clues in the example this was 6. If the linking square is part of a column clue Interchange column and row in the procedure given above.

Applying the rule The linking squares can be identified without looking at the clues. They depend only on the placement of the red and white squares.

We can say that the linking squares depend on the shape of the puzzle. We have circled the linking squares in the figure alongside. Start with the square Fd. This is part of a column clue. The sum of the column clues except the one it is part of is The difference is 3. It might seem that finding [Eh] is more complicated, but actually it is not. The square Eh is part of a row clue. This tool cuts finer The trick we have just developed actually cuts the puzzle into even smaller pieces.

You can easily convince yourself that you can figure out the values to be filled into the two squares which are circled in the picture alongside. Look at the square Gi. So Gi is a linking square. Finding the number to put down there is also strightforward. You can go through similar reasoning to convince yourself that Ef is also a linking square which should contain the value 9. With this the state of the puzzle is as shown above.

Now it is time to solve the eight simpler and smaller puzzles to which we have reduced this. Only eliminate Consider the simple sub puzzle at the top left corner, which is extracted here. So [Bb] can be one of 9 and 8, as shown in the figure alongside. The sub-puzzle shown alongside is solved in a similar way.

So [Gb] must be either 1 or 2. So this piece of the puzzle is also done. I leave this in your, by now, capable hands. The solution of Kakuro puzzles is helped along by several unique partitions.


Kakuro techniques

In addition, no number may be used in the same block more than once. The best way to learn how to solve Kakuro puzzles is to see how a puzzle is solved from beginning to end. Step 1 Kakuro puzzles are all about special number combinations. However, square a1 must be smaller than 6 because of the 6-in-two block in column a.



Numerical Puzzles For Your Brain Solve Kakuro puzzles In this guide we offer a range of practical tips on how to solve Kakuro puzzles, with difficulties ranging from beginner to expert level. In addition, inside each sum group, each digit can appear once at most. The traditional way to solve a Kakuro puzzle is incremental: by using the existing information on the board, you can find with certainty the value of a specific cell which can take only one possible value. Then that value is filled and the process is repeated until all the board cells have been discovered. In those cases each of the possibilities needs to be explored on its own and eliminated through contradictions until only one course of action remains. Usually you can hover on a Kakuro grid over the definition number and a tooltip will appear containing all the possibilities of writing that sum with unique digits in the number of available cells.


Tips and tricks: easy ways to solve Kakuro

You can eliminate this missing digit from all the cells. Any digits excluded from the missing digits must be in the word. Any digits which must be in the missing digits cannot be in the word. Since the two missing digits sum to 4, they must be 1 and 3. Therefore, the word contains the digits 2,4,5,6,7,8, and 9.

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