Another Kakuro strategy: difference of 2 cells
Last time I have had discussed about using arithmetics to solve kakuro (part 1, part 2); most of the methods are trivial for everybody except the last case which is not apparent. This one is also not apparent as well, and I have almost never encountered it except once. It is about:
Calculating the difference between 2 cells!
How can the difference of 2 cells be helpful? See below for initial configuration:
It is an open end layout, so using addition and subtraction seems not very feasible. There is also no apparent target with only one possible answer. Actually there is, but very well hidden. Calculate the sum of digits marked with green and red:
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Take the difference between red and green areas. The result is the difference of the 2 squares marked A and B, which is 4 ( = 38 – 34 ) :
So? There are still too many choices, 4 can be 5-1, can be 6-2, …… The key point is, only one of the choices is possible! Notice the 3rd row (with sum equal to 22), there are only 2 possible combinations, namely (5,8,9) and (6,7,9).
- B-A=4 ⇒ A ≤ 5
- From the 2 decompositions of 22 ⇒ A ≥ 5
Bingo! (A,B) = (5,9).
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tricky tricky!!
Wow, this is wonderful! I just started Kakuro yesterday. I’ve been doing Sudoku for years and I am pretty good at them. With Kakuro I started with easy puzzles, and you can figure them out with just addition and subtraction. The first open-ended puzzle I tried was very difficult…. hopefully I can try some of these techniques
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I would say the techniques are of intermediate to hard level. With addition and subtraction of areas, some of the seemingly difficult puzzles can be tackled quickly — though it is not always apparent to pick which area to do the subtraction. This technique is comparatively less documented, that’s why I’m giving more examples here. Indeed there are other tricks to be learnt as well!