PUZZLE TECHNIQUES

JAPANESE SUMS PUZZLE TECHNIQUES

Learn techniques for beginners and advanced players to solve Japanese Sums puzzle. We have a list of tips and tricks to get you started. These methods and strategies for solving Japanese Sums puzzles will also help you to solve other logic puzzles like sandwich sudoku, hitori, nurikabe, slitherlink, kakuro or suguru.

When you have studied our solving techniques, then it will be easier to play Japanese Sums puzzles online.

ROW OR COLUMN WITHOUT CLUES

Some puzzles have a row or column without clues. Then you need to make the sum of the clues of all the rows and the sum of the clues of all the columns. The difference will be the total of the missing clue(s).

There are NO clues in ROW 3. The total of the clues of all the colums is 36. The total of the clues of all the rows is 33. So the total of the clues in ROW 3 is 3. This means that there are three possibilities for ROW 3: we can have 3, 1-2 or 2-1 as clues.

CHECK THE LENGTH OF THE CLUES

It is best to start with to first or last row or column. In the example below we will check of we need more than one cell for the clues of the last column. Therefore we also need to look at the last clue of each row to see if it is possible.

We want to check if it is possible to place digit 5 or digit 6 in 1 cell in the last column.

• The last clue of row 1 is 2, so we can't place digit 5 in 1 cell.
• The last clue of row 2 is 8, so we can place digit 5 in 1 cell.
• If we place digit 5 in row 2, then the cell in row 3 must be black.
• The last clue of row 4 is 1, so we can't place digit 6 in 1 cell.
• The last clue of row 5 is 5, so we can't place digit 6 in 1 cell.

Conclusion: digit 6 must use 2 cells.

CHECK FOR POSSIBLE COMBINATIONS

Digit 6 has two combinations: 1-5 and 2-4. Because the last clue of row 4 is 1, we must use the 1-5 combination. Now we also see that we will need 2 cells for clue 5 in column 5, because we have alreday used digit 5 as part of clue 6.

The only possibility for clue 5 is the combination: 2-3. The last clue of row 2 is 2, therefore there is only 1 way to place the 2-3 combination.

THE SAME CLUES IN A ROW OR COLUMN

The digits 1 to 9 can be in 1 or more cells. Numbers 10 and higher always need 2 or more cells.

So when we have the same clues in a row or column, then one of them has to use more than 1 cell.

In row 3 we have 2 times clue 3. So we will need 3 cells in total.

• We use a circle to mark the outside cells as cells that will have a digit.
• We use a cross to mark the inside cells as cells the may become black.

In column 4 we only have 1 clue: digit 2.

• So the last cell of row 3 must be 2.
• Therefore the third cell of row 3 must be 1.
• The second cell of row 3 must be black.
• The first cell of row 3 must be 3.

PLACE CIRCLES AND MAKE CELLS BLACK

You can place a circle in a cell to indicate that this cell must contain a digit but at this moment you don't know the value of tha digit.

Make cells black when you are sure that they can't contain a digit.

In this Japanes sums puzzle we may only use the digits 1-6, so we need more than 1 cell for clue 7. Therefore we place 2 circles.

Clue 6 of column 2 can be completely in row 5 or in the cells of row 4 and 5. The only thing we know for sure that it has to be in row 5, so we place a circle.

We have found the correct cell for digit 2 in column 5. There are no other clues in that column, so all the other cells in that column must be black.

The first cell of column 3 can't contain 4, so it has te be black.