如何遊玩 殺手數獨
籠必須總和到給定總數——籠內沒有數字重複
Killer Sudoku arrived in British newspapers in 2005, imported from Japan where it had quietly existed for years as "samunamupure" — sum number place. The Times printed one, readers revolted at how hard it was, and then kept demanding more. That tension is still the variant's signature: a killer grid usually gives you no digits at all, only dashed cages with little totals in the corner, and yet everything you need is sitting right there in the arithmetic. It suits two kinds of solvers especially well. If you love kakuro or mental maths, the cage combinations will feel like home. If you're a classic Sudoku player who has plateaued, killer forces you to learn genuinely new deductions — above all the 45 rule, which turns the fixed total of every row, column, and box into a scalpel. What separates killer from other arithmetic variants is the no-repeat rule inside cages: it shrinks combination lists dramatically, so the maths stays manageable even when the grid starts empty.
規則
標準數獨規則適用： 用數字1–9填滿每一行、列和3×3宮，每個數字恰好出現一次。
殺手數獨在標準的9×9網格上疊加籠。每個籠是一組由虛線邊框勾勒的單元格，角落裡有一個小數字顯示該籠中所有數字的總和。數字不能在籠內重複。網格中不出現標準的給定數字——所有提示都來自籠總和。殺手數獨需要數獨邏輯和算術推理，使其成為最受歡迎和最具挑戰性的數獨變體之一。
如需了解此謎題的來源、與相關變體的比較及策略摘要，請參閱我們的 殺手數獨 變體概述.
一覽
如何解 殺手數獨
工作示例：打開一個 殺手數獨 謎題
Suppose the top-left box contains three complete cages: a three-cell cage totalling 15, a three-cell cage totalling 13, and a two-cell cage totalling 9 — eight cells accounted for, summing to 37. The box's nine cells must total 45, so the ninth cell, which belongs to a cage poking in from outside, is 45 − 37 = 8. One digit placed without a single given. Now look at that two-cell 9 cage: the 8 we just placed sits in a different cage but the same box, so the pair can't be {1,8} — only {2,7}, {3,6}, and {4,5} survive. Next, scan for a two-cell cage totalling 17 somewhere in the same band: it must be {8,9}, and since our box already holds its 8, the 17-cage's 8 fixes which row the band's remaining 8s avoid. This is the killer rhythm: a 45-rule deduction places a digit, the digit prunes a cage's combinations, the pruned cage behaves like a naked pair, and the eliminations set up the next 45-rule deduction one box over.
殺手數獨中的常見錯誤
| 錯誤 | 如何修正 |
|---|---|
| Ignoring the 45 rule and grinding cage combinations alone | Before enumerating anything, total the cages contained in each box, row, and column. The leftover innie or outie cell is pure profit — often a placed digit with zero combination work. |
| Forgetting the no-repeat rule when a cage crosses a box border | Digits can't repeat within a cage even where Sudoku rules alone would allow it. A four-cell cage totalling 26 can never be {9,9,4,4} — strike repeat-based combinations first and lists shrink fast. |
| Writing out every combination for big middle-value cages | A three-cell 15-cage has eight combinations; you'll drown. Start instead at the extremes — 2-cell cages of 3, 4, 16, 17 and 3-cell cages of 6, 7, 23, 24 — which have one or two combinations and anchor everything else. |
常見問題
什麼是殺手數獨？ ▾
Killer Sudoku combines standard Sudoku with arithmetic cage clues. The grid is divided into cages — groups of cells outlined by dashed borders — each with a small number in the corner. The digits in each cage must sum to that number, and no digit may repeat within a cage. Standard Sudoku rules also apply throughout.
What is the 45 Rule in Killer Sudoku? ▾
Every row, column, and 3×3 box contains the digits 1–9, which sum to 45. If you know the total of cages that sit entirely within a unit, you can deduce the sum of any partial cage cells crossing the boundary. These leftover cells are called 'innies' (inside the unit) or 'outies' (outside), and they often resolve to a single digit immediately.
Can I start solving without any given digits? ▾
Yes — Killer Sudoku typically has no pre-filled digits. All information comes from cage sums and Sudoku rules. Start with cages that have only one possible combination: a 2-cell cage summing to 3 can only be {1,2}, and a 2-cell cage summing to 17 can only be {8,9}. Apply the 45 Rule to each unit to find more placements.
How is Killer Sudoku different from Arrow Sudoku? ▾
In Killer Sudoku, digits within a cage must sum to the clue and cannot repeat within the cage. In Arrow Sudoku, digits along an arrow sum to the circle and can repeat. Killer cages are irregular shapes scattered across the grid; arrow cells follow a linear path from a circle.
殺手數獨比普通數獨更難嗎？ ▾
Most players find Killer Sudoku harder than classic Sudoku at equivalent difficulty labels. Easy Killer puzzles are comparable to hard classic Sudoku. The arithmetic layer adds complexity, but cage constraints also provide more starting information than simple given digits once you learn to exploit them fully.
How long does Killer Sudoku take to solve? ▾
Easy puzzles take 10–20 minutes. Medium puzzles run 20–40 minutes. Hard puzzles average 40–75 minutes and expert puzzles often exceed 90 minutes. Applying the 45 Rule fluently is the single biggest factor in improving solve speed.