Archive for February, 2008

As discussed in previous post, kakuro can be tackled using simple addition and subtraction during initial stage, particularly if the kakuro puzzle contains some certain arrangement pattern. As an example, see the figure below:

With arithmetics, one can deduce A=1 and B=3. This method, though less likely mentioned in general kakuro strategy guide, has been presented in Wikipedia page. Generally, this method is only usable when an area is enclosed, and there is only one single outlet among all those squares. In the above puzzle the outlet is square A. Thus such method is not useful in the next puzzle below:

Does it mean addition and subtraction will be completely useless then? Not entirely, depends on situation. Under rare circumstances, addition and subtraction might be useful even during mid-games or end-games. The diagram below shows the stage when large part of above puzzle is solved:

Here comes the tricky bit: concentrate on upper right area. We are not getting the value of a single square, not even sum of two squares, but three.

Take summation of all red squares horizontally, then deduct all deeper red squares vertically, one gets A+B+C=21. So what? 21-in-3 has too many combinations, and it’s still hard to try one by one. The key here is, value of A has great limitation. See the final figure below, and observe the square marked “x”:

Within the column with sum=32, there is a ‘2′, thus this column has only one single combination: (2,6,7,8,9), which means x=6 or 8 or 9. Is it true? No. If x=6, then A=6, and violates kakuro rule.

That means x=8 or 9, implying A=3 or 4. But recall that A+B+C=21. If A=3, then B=C=9, game over. So we get the answer: (A,B,C) = (4,9,8).

Sort of puzzled — I haven’t seen anywhere mentioning that some kakuro puzzles can be solved with the help of simple arithmetics (yet). Indeed I don’t mean the whole puzzle can be solved merely with addition and subtraction; nor do I mean every puzzle can be worked on this way. Arithmetics usually only works at the beginning, and only works with some kind of puzzles. Here is a simple example. Consider the following fragment:

It’s solvable without any arithmetics; but hey, I’m just illustrating how to do it in other way, and (arguably) easier way. Look at the diagram below:

Look at the 2 rows marked with green arrow, and 2 columns marked with cyan arrow. One get A + B = 22 + 8 - 11 - 7 = 12. Still, some more hints are needed. Now look at the column with sum = 35. Since 35 has only one combination (5, 6, 7, 8, 9), in order to pick 2 numbers out of these 5 and satisfying A + B = 12, viola, we have A=7 and B=5. Not hard, isn’t it?

2008-02-29: Next post on solving kakuro with arithmetics here.

比之前提及來自 Mandriva 那一封電郵更過癮。今次有可能是來自俄羅斯、白俄羅斯之類的國家的。內容也很簡單，只是問我還有沒有任何 0-day exploit (請看英文解釋，中文維基那篇是垃圾來的)，如果有的話，想我開個價錢。詭異至極。可能是因為上次 disclose 了 WordPress 的漏洞的緣故吧。

前幾天收到一封有點詭異的電子郵件，是來自 Mandriva 其中一個開發人員的。他在郵件中問我，要不要回去重新參與 Mandriva 的開發。那個人也大概知道，是因為 Mandriva 另一個開發人員多番侮辱，再加上不滿那種各開發人員割地分封的管理手法，我才離開的。

固然，在 internet 的世界，不用說十年人事幾番新了，一兩年已經足夠：大部分 Mandriva 的老臣子都走了 (尤其 Warly 離開得有點……醜陋)，聽聞更大部份由 contributor 管理，架構和 release 的制度都好像不同了，當初不滿意的地方，現在未必還是那樣子；只是自己現在還有沒有那種心，那種力，就是另一回事了。