# KENDOKU

Originally developed as a math tutoring puzzle, Kendoku is an interesting and challenging variation of the classic Sudoku.

In Kendoku, random cells are grouped together. For these groups, an arithmetic operation and the result is displayed as a solution guide. To solve the puzzle, the player must deduce the number they are looking for from these clues.

# Terms

## Group

A group is marked in orange. Its result is -1. The arithmetic operation is subtraction. The group consists of 4 cells, one of which is already revealed.

## Group

A group is marked in orange. Its result is -1. The arithmetic operation is subtraction. The group consists of 4 cells, one of which is already revealed.

## Column and Row

In the example, one row (horizontal) and one column (vertical) are highlighted.

## Column and Row

In the example, one row (horizontal) and one column (vertical) are highlighted.

## Cell

A cell is a single number that is either a given, already solved, or still hidden. It can also be designated by its coordinate number. It is usual to assign letters to the columns (so in the example A to F) and numbers (1 to 6) to the rows.

In this example, the already uncovered 4 therefore have the coordinate D4, the highlighted cell is at coordinate C3.

## Cell

A cell is a single number that is either a given, already solved, or still hidden. It can also be designated by its coordinate number. It is usual to assign letters to the columns (so in the example A to F) and numbers (1 to 6) to the rows.

In this example, the already uncovered 4 therefore have the coordinate D4, the highlighted cell is at coordinate C3.

# Variants

One Sudoku offers Kendoku puzzles in sizes 3x3 to 6x6. Four difficulties are available for the larger variants. The small sizes 3x3 and 4x4, suitable for beginners, are available in Easy and Advanced.

The variants differ in the arithmetic operations (division is required in Expert and Challenging) and the allowed order for subtractions (Easy: only from large to small, for example 6 - 4 - 3, from Challenging onwards other orders can be considered). Starting from the difficulty level Challenging, groups can also contain the same number more than once.

# Rules

Unlike in classic Sudoku, boxes do not play a role in Kendoku. For a 4x4 Kendoku puzzle, therefore, the following applies: in each column and each row, each number from 1 to 4 may occur only exactly once.

Unlike in classic Sudoku, boxes do not play a role in Kendoku. For a 4x4 Kendoku puzzle, therefore, the following applies: in each column and each row, each number from 1 to 4 may occur only exactly once.

# Solving Steps

## Step 1

In this example of a 4x4 Kendoku there are 7 groups. Two of them extend over three cells and are to be solved as multiplication.

## Step 1

In this example of a 4x4 Kendoku there are 7 groups. Two of them extend over three cells and are to be solved as multiplication.

## Step 2

In the group of 2 at the bottom right, the result of a multiplication is three. Since for possible candidates 1 to 4 only the calculation 1 x 3 is possible, 2 and 4 can be excluded as candidates for the solution. The reason is that all other possible combinations (1 x 2, 1 x 4, 2 x 3, 2 x 4) do not have 3 as a result.

## Step 2

In the group of 2 at the bottom right, the result of a multiplication is three. Since for possible candidates 1 to 4 only the calculation 1 x 3 is possible, 2 and 4 can be excluded as candidates for the solution. The reason is that all other possible combinations (1 x 2, 1 x 4, 2 x 3, 2 x 4) do not have 3 as a result.

## Step 3

Using the pair 1 and 3 in the bottom two cells, we can now enter the two remaining numbers 2 and 4 in column D above as possible solutions.

## Step 3

Using the pair 1 and 3 in the bottom two cells, we can now enter the two remaining numbers 2 and 4 in column D above as possible solutions.

## Step 4

Since the top two cells in column D belong to a group of 3, we can reveal the first number for the other cell of this group C1. Since 2 x 4 is already the result of the multiplication, the last number can only be 1.

## Step 4

Since the top two cells in column D belong to a group of 3, we can reveal the first number for the other cell of this group C1. Since 2 x 4 is already the result of the multiplication, the last number can only be 1.

## Step 5

In column C below the first solution, the result of a multiplication is 6. With possible candidates 1 to 4, only the 3 and the 2 (3 x 2 = 6) come into question here.

## Step 5

In column C below the first solution, the result of a multiplication is 6. With possible candidates 1 to 4, only the 3 and the 2 (3 x 2 = 6) come into question here.

## Step 6

This leaves only 4 in column C as the only solution for the lowest cell C4.

## Step 6

This leaves only 4 in column C as the only solution for the lowest cell C4.

## Step 7

Due to the revealed 4 in the group of two with a multiplication and the result 8, the 2 can be entered into the second cell B4 of this group as the only possible solution (2 x 4 = 8).

## Step 7

Due to the revealed 4 in the group of two with a multiplication and the result 8, the 2 can be entered into the second cell B4 of this group as the only possible solution (2 x 4 = 8).

## Step 8

In the lower group of the first column A, the addition with the result 7 allows only 3 and 4 as possible candidates, all other calculation combinations do not lead to the required result.

In row 4, the 1 can therefore only be entered in cell D4. Thus we can uncover this group and in cell A4 the 3 as the last remaining number of this row. Thus we can additionally solve the group in column A.

## Step 8

In the lower group of the first column A, the addition with the result 7 allows only 3 and 4 as possible candidates, all other calculation combinations do not lead to the required result.

In row 4, the 1 can therefore only be entered in cell D4. Thus we can uncover this group and in cell A4 the 3 as the last remaining number of this row. Thus we can additionally solve the group in column A.

## Step 9

This leaves the numbers 1 and 2 for column A, which we can enter as candidates in the upper group. However, since the 1 in cell C1 is already solved, it is omitted as a candidate for cell A1.

Also, by looking at the result x6, we can see that in addition to 1 and 2, we also need a 3 to arrive at this result. Since the other two cells of the group are already occupied, only cell B1 remains for the 3.

## Step 9

This leaves the numbers 1 and 2 for column A, which we can enter as candidates in the upper group. However, since the 1 in cell C1 is already solved, it is omitted as a candidate for cell A1.

Also, by looking at the result x6, we can see that in addition to 1 and 2, we also need a 3 to arrive at this result. Since the other two cells of the group are already occupied, only cell B1 remains for the 3.

## Step 10

Thus we can uncover all numbers for this group. For the last remaining group, there is also only one possible solution in each case, so that the rule that each line may only contain the numbers from 1 to 4 exactly once is not violated.

## Step 10

Thus we can uncover all numbers for this group. For the last remaining group, there is also only one possible solution in each case, so that the rule that each line may only contain the numbers from 1 to 4 exactly once is not violated. 