  
Kakuro example
Let's solve a puzzle together. Generally, we first look for cells with minimum possible alternatives.


Step 1. Very helpful is to discover unique combinations in the puzzle like the two intersecting sequences highlighted with blue and red on the picture. The only 2cell combination with sum 3 is 3 = 1+2. Analogously, 4 = 1+3. So, the value of the intersecting cell must be 1.

Step 2. Now, take a look at the intersection on the next picture. Again we have a unique combination at the down clue (10 = 1+2+3+4), so the maximal possible value for each cell in this sequence is 4. Although there are many possible combinations for the across clue (13 = 4+9 = 5+8 = 6+7), the minimal possible value for each cell in that sequence is 4. Therefore, for the intersecting cell, there is no other possible value except 4.



Step 3. The next highlighted clues show a similar situation  intersection between unique combination sequences (23 = 6+8+9 and 16 = 1+2+3+4+6), where the only possible value for the intersecting cell is 6.

Step 4. Now, let's analyze the blue highlighted sequence. As we mentioned, the only possible combination here is 16 = 1+2+3+4+6. So, we have 3 empty cells  the second, the fourth and the fifth  and 3 missing values  1, 2 and 4. If we look for the right cell for the 4, we will exclude the second one, because the 4 already exists in the down sequence. We will also exclude the fourth one, because 4 doesn't appear in the possible cell values of the down clue (11 = 1+2+3+5). Therefore, the 4 must be placed in the fifth cell of the sequence. Afterwards, the 2 already appears in the down sequence along the fourth cell, so we will place it in the second cell.



Step 5. Look at the red highlighted down sequence. As we mentioned, the only possible combination here is 11 = 1+2+3+5. The remaining empty cells must be filled with 3 and 5. But 5 can't appear in the blue highlighted across sequence, because the entire sum of the sequence is 5.

Step 6. At last, the missing 1 and 3 in the highlighted sequence can fill the empty cells in only one way, thus making the rest of the solution obvious.



Congratulations! We have a solved puzzle.



Copyright © 2012 Boyan Kolev, Sofia, Bulgaria
