Another Kakuro strategy: difference of 2 cells
2008-08-09Last 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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