The Miracle of Kakuro Blocks
Kakuro Blocks are special cases that have one and only one combination. When you see these blocks, you know there is only one possible set of numbers that fit, and all you have to do is worry about the order. Kakuro Blocks are lovely, and by the time you've done a few Kakuro puzzles you will see them in your sleep.
Here are some of them:
| Target | Squares | Combination |
| 3 | 2 | { 1, 2 } |
| 4 | 2 | { 1, 3 } |
| 16 | 2 | { 7, 9 } |
| 17 | 2 | { 8, 9 } |
| 6 | 3 | { 1, 2, 3 } |
| 7 | 3 | { 1, 2, 4 } |
| 23 | 3 | { 6, 8, 9 } |
| 24 | 3 | { 7, 8, 9 } |
| 10 | 4 | { 1, 2, 3, 4 } |
| 11 | 4 | { 1, 2, 3, 5 } |
| 29 | 4 | { 5, 7, 8, 9 } |
| 30 | 4 | { 6, 7, 8, 9 } |
There are more, for blocks with 5, 6, 7, 8 and 9 squares, but we'll worry about them later. For now these will be enough to get you started. Look out for these blocks in any Kakuro puzzle, and you'll almost always find your starting point - we'll show you how in a moment.
Unique Intersects
This is the first technique, and almost certainly the most useful. It works like this:
If two Kakuro blocks cross a square, and they have only one number in common,
then the value in that square must be that number.
Let's have a look at the puzzle:
We want to find Kakuro Blocks (that is, blocks with only one possible combination) that cross. Block E6 Across is a Kakuro block (it has a Target of 4 with two cells - what we call 4-in-2) and it crosses D7 Down, which is another Kakuro block - 3-in-2.
This is great! Look back at the Kakuro Block list - 3-in-2 can only contain the numbers { 1, 2 } and 4-in-2 can only contain { 1, 3 }. The only number they have in common is 1, so where they cross (E7) the value in the cell has to be - 1!
One down, 20 empty squares to go. Can you see any more Unique Intersects?
Here's another one. Block D2 Across (17-in-2) is a Kakuro Block, and so is D2 Down (16-in-2).
17-in-2 has only one combination: { 8, 9 }
16-in-2 has only one combination: { 7, 9 }
They only share one number in common, so where they cross - D2 - must be a 9.
And there are some more Unique Intersects, here:
Here are two more cases, both with the same pair of Kakuro Blocks. In B4 Across, the block is 23-in-3 - that is, a Target of 23, with three cells. B4 Down is 16-in-2.
23-in-3 has only one combination: { 6, 8, 9 }
16-in-2 has only one combination: { 7, 9 }
They only share one number - 9 - and it has to be where they cross, at B4. We can do the same with blocks G3 Across and F4 Down, and when we do we can see we now have this board:
So far, so good. Let's fill in some of the blanks.
If B4 Down adds up to 16, and we have the 9, then the remaining square must be 7.
If D2 Across adds up to 17, and we have the 9, then the remaining square must be 8.
If D7 Down adds up to 3, and we have the 1, the remaining square must be 2.
If D2 Down adds up to 16, and we have the 9, the remaining square must be 7.
If F4 Down adds up to 16, and we have the 9, the remaining square must be 9.
Here we are:
We're doing pretty well, and we can do more - now we've filled in some of the blanks, we can see where other values can go, like this:
Unfortunately, that's the end of our free ride. We've found all the Unique Intersects, and we've filled in all the easy gaps. Now what?
...We'll tell you on the next page.
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