Killer Sudoku Rules and Strategy

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Killer Sudoku is what you get when you cross ordinary Sudoku with a dash of arithmetic. The grid starts completely empty, which sounds terrifying and turns out to be a lot of fun once the trick clicks.

What stays the same

Everything you know about classic Sudoku still holds. It's a 9×9 grid, and every row, column, and 3×3 box must end up with the digits 1 to 9, none repeated. If you haven't met those rules yet, read how to play Sudoku first — the rest of this page assumes them.

What's new: cages

Instead of starting numbers, a Killer grid is covered in cages: little groups of cells outlined by a dotted border, each printed with a small total in one corner. The deal is simple — the digits you place in a cage have to add up to that total, and within a single cage no digit repeats.

That last bit catches people out. A cage of two cells marked 10 can't be 5 and 5; it has to be two different digits, so 4+6, 3+7, 2+8, or 1+9. The no-repeat rule inside a cage is on top of the usual row, column, and box rules, not instead of them.

The 45 rule

Here's the lever that makes Killer solvable. Every row, column, and box contains 1 through 9 exactly once, and those digits add up to 45 — always. So if a box is neatly carved into cages totalling, say, 12, 18, and 9, those add to 39, and the one cell sticking out must hold 45 − 39 = 6. You just placed a digit with pure bookkeeping, no candidates required.

The 45 rule scales up and down. Two full rows total 90. A box plus an overlapping cage can be subtracted from each other. Whenever the cages line up almost-but-not-quite with a unit, the leftover is where the arithmetic pays off.

Combinations worth memorising

Some cages can only be filled one way, and knowing them on sight is half the battle. The extreme totals are the friendliest:

Even when a cage has a couple of options, the arithmetic narrows the field fast. A two-cell cage of 16 is either 7+9 — and that's it (no 8+8 allowed). Spot one of those and you've locked two cells down to a tiny menu before you've looked at a single row.

How to start an empty grid

With no givens, you hunt for the most constrained cages first — the 3s, the 17s, the long cages with tiny totals. Pencil in their forced combinations, then let normal Sudoku logic take over: those committed digits start knocking candidates out of their rows, columns, and boxes, and suddenly the grid behaves like the Sudoku you already know. The 45 rule is your crowbar for the moments when the candidates alone won't budge.

Give it a go

Reading about cages only gets you so far. Open a Killer puzzle and ask the AI tutor for a hint whenever you stall — it'll show you exactly which cage or unit it leaned on and why the number was forced.

Killer 数独规则与策略

Killer 数独，就是把普通数独和一点点算术杂交出来的产物。盘面一开始空空如也，听着吓人，可一旦窍门通了，反而特别上瘾。

不变的部分

你对经典数独的认识照样成立。还是 9×9 的盘，每一行、每一列、每个 3×3 宫，最后都要填齐 1 到 9 且不重复。要是你还没搞清这些规则，先去看数独怎么玩——这一页默认你已经会了。

新东西：笼

Killer 盘上没有初始数字，取而代之的是「笼」：一小撮被虚线圈起来的格子，角上印着一个小小的总和。规矩很简单——你填进一个笼里的数字，加起来要等于那个总和，而且同一个笼里数字不能重复。

最后这点常把人坑到。一个标着 10 的双格笼不能是 5 和 5，必须是两个不同的数，所以只能 4+6、3+7、2+8 或 1+9。笼内不重复这条，是叠加在原本的行、列、宫规则之上的，不是用来替换它们。

45 法则

这是让 Killer 能解开的那根撬棍。每一行、每一列、每一宫都恰好含 1 到 9 各一次，它们加起来是 45——永远如此。所以如果某个宫被整齐地切成总和为 12、18、9 的几个笼，这几个加起来是 39，那个多出来的孤格就必然是 45 − 39 = 6。你靠纯记账就落了一个数，连候选数都不用动。

45 法则能放大也能缩小。两整行加起来是 90；一个宫和与它部分重叠的笼可以相减。每当笼跟某个单元「几乎对齐又差一点」时，那点多出来的部分，就是算术发威的地方。

值得背下来的组合

有些笼只有一种填法，一眼认出它们，仗就赢了一半。和最极端的那几个最好认：

就算一个笼有那么两三种选项，算术也能很快把范围掐窄。一个总和 16 的双格笼，只能是 7+9——就这一种（不许 8+8）。瞅见一个这样的笼，你还没看任何一行，就已经把两格锁进了一份极短的菜单里。

空盘怎么开局

既然没有初始数字，那就先去找约束最狠的笼——那些 3、那些 17、那些和小却格多的长笼。把它们被逼出来的组合先用铅笔记上，然后交给常规数独逻辑接手：这些定下来的数字开始从各自的行、列、宫里敲掉候选，一转眼，盘面就变回你熟悉的那个数独了。而 45 法则，是候选数死活推不动时，你那根撬棍。

动手试试

光读笼的概念，能走的路有限。开一局 Killer，卡住了就找 AI 导师要提示——它会明确告诉你它靠的是哪个笼或哪个单元、那个数又为什么是被逼出来的。