Reducing Combinations
B5 Down (14-in-2) isn't a Kakuro Block, but it does cross one. In fact, it crosses two, and that's a good start. We've already looked at B4 Across, a 23-in-3, and we know it has only one combination - { 6, 8, 9 }. C3 Across is yet another Kakuro Block - with a target of 29 over four cells, the only possible combination is { 5, 7, 8, 9 }.
Armed with these facts we can reduce the number of combinations for B5 Down.
We know the block is a 14-in-2 - that is, it has a Target of 14, spread over two cells. The possible combinations are:
6 + 8 = 14
5 + 9 = 14
But can they both fit? Let's try them out. 6 + 8 could fit - the 6 could go on the top row, and the 8 underneath. But what about 5 + 9?
The 5 can't go on the top row, because we know the only combination for the top row is { 6, 8, 9 }. The 5 could go on the second row ( C3 Across ). But then the 9 would have to be on the top row - and we already have a 9 on that row... So no-go.
We've reduced the combinations down to one - { 6, 8 }. Better still, we even know the right order, because only the top row has a '6' in its combination. We can place both the values, like this:
We're on the home straight now. B6 has to be 8, so we'll put that in. And we can put together what we've learned to solve the rest, like this:
C3 Across is a Kakuro Block with only one combination - { 5, 7, 8, 9 }, and the 9 is locked to square C6 (try to work out why)...
...Which leaves C3 Across with only one space left - C3 - so that must be where the 5 goes...
...Which leaves C3 Down with only one space left - F3 - and since the Target is 32, and the numbers already in place add up to 28, F3 must be a 4..
...And so F6 Across must be a 2...
...And the board is solved! Well done. Have a beer.
Here's the final, solved board:
Piece of cake. Remember:
- A number can't appear twice in the same block
- You never have to guess
- Kakuro Blocks Are Your Friends
Now you know what to do, have a go at our Daily puzzles. They're graded from Delicious to Atrocious, so you can start on the weedy boards till you get your skills up to scratch and then try for something a bit more adventurous. And our Kakuro-san Assistant can help you out with logical advice if you get stuck.
Have fun!