Sums puzzle is about filling the board with digits so that each digit is only one time in each row and column.
In each row (column) every digit must be used. Digits separated by empty field create groups.
The sum of digits in a concrete group must respond to the figures presented outside the diagram.
In particular puzzles can be digits from 1 to 4, 1 to 6, 1 to 9 etc.
Higher number of digits doesn’t increase the difficulty of puzzles.
You should start solving a puzzle from rows or columns with low or high figures.
Sums puzzles are quite similar to Sudoku. You can also use methods of Kakuro and nonograms puzzles. As a result solving of Sums puzzle involves many strategies and methods.
Online solving:
When you click on any field of board, you will see the menu with following options to chose:
- „-” – symbol of movement cancelation,
- „*” - symbol of digit being in particular field,
- „X” - symbol indicating absence of a digit,
- „1, 2, 3, 4, 5, 6 ....” - digit, which will be put in field.
Moreover, when you click on figures presented outside the diagram, you will “unmark” them (it’s mean that particular group of digits are completed).
You can also use the option "Clear" from Helper.
An example puzzle:
Fill the board with digits from 1 to 4.
In the first row there is one group of digits, in which sum is 10.
In the first column there are two groups of digits. One (from the top) with sum of 6 and second one – 4.
Solution:
Hints:
- The group with sum of digits: “1” can be placed on the board only in one option: as a digit 1.
- The group with sum of digits: “2” can be placed on the board only in one option: as a digit 2.
- The group with sum of digits: “3” can be placed on the board in three combinations: as a digit 3, digits 1, 2 or as a digits 2, 1.
- The number of digits in group is not known, but it is possible to calculate the maximum and minimum number of digits e.g. on the board with digits from 1 to 4, group of digits “8” must consist of 3 digits at least.
- Group of digits can consist of maximum three digits (1+2+3).
- At the beginning of solving a puzzle it is rather difficult to put a particular digit on the board. That’s why you should find fields where digit will appear or not (X).
- On the basis of advice above, you are filling board with digits or marking fields where a digit will appear.
Solving methods of logical puzzle – Sums.
If you visit this page for the first time, we advise you to choose some puzzles from “easy” category. While solving you will discover methods yourself.
When you have got a problem with starting or solving puzzle, look at the followings methods.
The following methods are supported by an exemplary boards 10x10 digits, where digits from 1 to 6 must be placed.
Method no. 1
First of all, look at columns/rows where is one group of digits (this is not the case in every puzzles).
This group must consist of all digits (in our case six digits).
On the diagram below, in the first column (on the left), group with sum of digits „21” can be placed only in one way as a 6-digit sequence. When you place it on extreme positions (one from the top and second one from the bottom), you can see that in two fields there will always be digits. You still don’t know what digit will be placed, but you will discover it in the next steps of solving.
Method no. 2
Just as in method no. 1, you are looking for groups which are “overlapping”.
Analyze each column (row):
- In each column (row) there are six digits and also necessary gaps between groups of digits;
- The received value describes minimum number of fields you need in particular column (row);
- Count value above from the top (from the left) and the minimum number of digits for the extreme group on the bottom (on the right);
- Mark the common part (if it exists);
- Repeat this calculation for the opposite direction – from the bottom (from the right).
You can see the method no. 2 on the following diagram:
Analyze second column on the left with groups of digits: 9, 3,2, 7. You have to use six digits and three gaps between them (9 fields).
When you calculate this number from the top, you will stop on the ninth field. The extreme group of digits on the bottom is “7”.
It means that you need at least two digits to create the group “7”. Count this group from the bottom. You can see that the common part is one before the last field.
Do the same calculation for the group of digits “9”. Similarly, the common part is one field.
When you get to know how it works, you will use this method not only to extreme groups of digits.
Method no. 3
This method is about lengthening particular group of digits on the board. It is possible when as a consequence of other methods one or more field (belonging to the group) will be marked.
On the following diagram you can see that as a result of method no. 2, one field was marked. It belongs to group of digits “21” in the first row. You can mark next four fields, because this group consists of six digits,.
Method no. 4
When in a particular column/row there is field with digit (or only marked), it is possible that you can’t place any digit on the other side of column/row. It is equivalent to the „X”.
You can continue our example. You can see that in row with group of digits “21” you can’t place digits in the last three fields on the right.
Group of digits “21” consists only of 6 digits, not nine.
Method no. 5
Group of digits with highest number of digits needs a certain number of digits. For example group of digits “15” needs at least three digits (6+5+4).
It means that in some situations it will be impossible to place group in a particular field.
When you look at our board, you can see it in second column on the right. Group of digits “14”consists of at least three digits. On the board there is only one empty field. It means that this group can’t be placed there. That’s why you can put “X”.
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