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# Kakuro rules

The game of Kakuro is also called Cross Sum puzzle. Look at the game rules.

The Kakuro puzzle is of different size of length and width, although most puzzles are squares.

The Kakuro has 3 different boxes.

• A clue box – which has usually a number on the bottom and/ or on the right side.
• A white blank box – that is where you fill in the a number between 1 and 9.
• A block box – that is the black box.

Rule :
Place one digit from 1 to 9 in each empty box so that the sum of the digits in each set of consecutive white boxes(horizontal or vertical) is the number appearing to the left of a set or above the set. No number may appear more than once in any consecutive boxes.

The Kakuro puzzle has a significant relation between the number of boxes and the sum of the boxes.
As the simple example the 3 on 2 boxes. This can have only one combination of numbers 1 + 2. Once mastering this table the puzzle becomes more logical to solve.

 number of boxes sum combination 2 3 1+2 4 1+3 16 7+9 17 8+9 3 6 1+2+3 7 1+2+4 23 6+8+9 24 7+8+9 4 10 1+2+3+4 11 1+2+3+5 29 5+7+8+9 30 6+7+8+9 5 15 1+2+3+4+5 16 1+2+3+4+6 34 4+6+7+8+9 35 5+6+7+8+9 6 21 1+2+3+4+5+6 22 1+2+3+4+5+7 38 3+5+6+7+8+9 39 4+5+6+7+8+9 7 28 1+2+3+4+5+6+7 29 1+2+3+4+5+6+8 41 2+4+5+6+7+8+9 42 3+4+5+6+7+8+9 8 36 1+2+3+4+5+6+7+8 37 1+2+3+4+5+6+7+9 38 1+2+3+4+5+6+8+9 39 1+2+3+4+5+7+8+9 40 1+2+3+4+6+7+8+9 41 1+2+3+5+6+7+8+9 42 1+2+4+5+6+7+8+9 43 1+3+4+5+6+7+8+9 44 2+3+4+5+6+7+8+9 9 45 1+2+3+4+5+6+7+8+9

Hints

1) no double numbers

How to solve:

We take here a easy example :

Step 1. Step 1.

There are 2 clues for the A box, 7 for the top and 6 for the left.

We know that to get a 6 with the combination of 4+2 and 5+1. Meaning the number 1,2,4 , or 5 will be in box A.

Step 2.

We look now to the left, box B. There we have the clues on top 3, and left 6. We know that to get a 3 the only combination that can be is 1+2.

Step 3.

In box D, there the clue 3 to the top and clue 4 to the left. We know that 3 is 2+1. And that 4 is 3+1. So the number 1,2, or 3 can be in box D.

Step 4.

In box C, we have the 4 to the left and 7 on top. The combination for 4 is, 3 +1 .
Here we can conclude that in D 2 is eliminated from the possible solutions because in to make a 4 there is no 2.

Looking to the top of C, a 7. the combinations of 1+6, 2+5, 3,+4.
Now 1+6 is not a possibility because A can not hold a 6, step 1. Also 2+5 is not an answers, because in D can only be 3 or a 1.

As a consequence 3 is the only possible solution for C. as a consequence D is 1, and B is 2. The only possibility for A is 4. 