# Killer & Jigsaw Sudoku Rules

## Solving Guide

### (Killer Sudoku  PuzzlesRules - see below)

(Jigsaw Sudoku  Puzzles  Rules - see below)

Killer Sudoku Rules

Introduction
Killer Sudoku (also known as killer su doku, sumdoku, sum doku, addoko, or samunamupure) is derived from sudoku and kakuro. First developed in Japan in the mid 1990s as “samunamupure” (translated to 'sum number place'), the puzzle has been 'labeled' by the London Times as a 'killer' puzzle due to its complexity & frustrating complexity.

Fig. 1  Killer Sudoku Puzzle

Terminology
- cell -- a single square that contains one number in the puzzle
- row (r) -- a horizontal line of 9 cells
- column (c) -- a vertical line of 9 cells
- nonet (N) -- a 3x3 grid of cells, outlined by borders (also referred to as a 'box' in Sudoku puzzles). The term nonet eliminates potential ambiguity between the words “box” and “square”
- cage -- a group of internal cells outlined by a dotted line (or by individual colours)
- Abbreviated cell description: To describe a cage with a sum of 23 that spans 3 cells, one could use a 'longhand' description of
“23-sum 3-cell cage”, but for brevity I'll describe this as “23(3)”, and the set of those 3 numbers can be as an ordered set: [689] (i.e. in square brackets - required in exactly that order), or as {689} (with curly brackets, to denote an unordered set in any order)
- region (or house) -- any non-repeating set of 9 cells (can be used as a general term for 'row, cell or nonet', and in Diagonal Killer (similar to X-Factor Sudoku) as 'long diagonal')

Rules
The objective is to fill the puzzle grid with numbers from 1 to 9 so that the following conditions are met:
- Each row, column and nonet contains each number exactly once;
- The sum of all numbers in a cage must match the small number printed in the cage's upper left corner;
- No number is repeated in a cage (i.e. no cage can contain more than 9 cells but may overlap nonets);
- In Diagonal Killer Sudoku (also known as 'Killer X'), each of the long diagonals contains each number once;

- Rule of 45: Each Sudoku region contains the digits one through nine, adding up to 45. If X is the sum of all the cages contained entirely in a region, then the cells not covered must sum to 45-X. By adding up the cages and single numbers in a particular region, one can deduce the result of a single cell. If the cell calculated is within the region itself, it's referred to as an 'innie' (Fig. 1 - the top-left nonet has 1 innie from 9(2)); if outside the region, it's called an 'outie' (Fig. 1 - top-right nonet has outties from 36(6)). The 'rule of 45' can be extended to calculate the innies or outies of N adjacent regions - as the difference between the cage sums and N*45. Often it's useful to derive the sum of 2 or 3 cells, then use other elimination techniques.

Hints
- Since Killer Puzzles are derived from regular Sudoku Puzzles, don't totally rely on Killer Sudoku rules alone to solve a Killer Sudoku puzzle - use common Sudoku solution techniques as well (i.e. Naked/Hidden Pairs, X-Wing, Colouring, Swordfish, Forcing Chains etc.) may well help you to solve the most difficult Killer Sudoku puzzle;

- Look for the Fewest Possible Combinations
 3 12 3 4 13 4 5 14 23 5 6 15 24 123 6 7 16 25 34 124 7 8 17 26 35 125 134 8 9 18 27 36 45 126 135 234 9 10 19 28 37 46 127 136 145 235 1234 10 11 29 38 47 56 128 137 146 236 245 1235 11 12 39 48 57 129 138 147 156 237 246 345 1236 1245 12 13 49 58 67 139 148 157 238 247 256 346 1237 1246 1345 13 14 59 68 149 158 167 239 248 257 347 356 1238 1247 1256 1346 2345 14 15 69 78 159 168 249 258 267 348 357 456 1239 1248 1257 1347 1356 2346 12345 15 16 79 169 178 259 268 349 358 367 457 1249 1258 1267 1348 1357 1456 2347 2356 12346 16 17 89 179 269 278 359 368 458 467 1259 1268 1349 1358 1367 1457 2348 2357 2456 12347 12356 17 18 189 279 369 378 459 468 567 1269 1278 1359 1368 1458 1467 2349 2358 2367 2457 3456 12348 12357 12456 18 19 289 379 469 478 568 1279 1369 1378 1459 1468 1567 2359 2368 2458 2467 3457 12349 12358 12367 12457 13456 19 20 389 479 569 578 1289 1379 1469 1478 1568 2369 2378 2459 2468 2567 3458 3467 12359 12368 12458 12467 13457 23456 20 21 489 579 678 1389 1479 1569 1578 2379 2469 2478 2568 3459 3468 3567 12369 12378 12459 12468 12567 13458 13467 23457 123456 21 22 589 679 1489 1579 1678 2389 2479 2569 2578 3469 3478 3568 4567 12379 12469 12478 12568 13459 13468 13567 23458 23467 123457 22 23 689 1589 1679 2489 2579 2678 3479 3569 3578 4568 12389 12479 12569 12578 13469 13478 13568 14567 23459 23468 23567 123458 123467 23 24 789 1689 2589 2679 3489 3579 3678 4569 4578 12489 12579 12678 13479 13569 13578 14568 23469 23478 23568 24567 123459 123468 123567 24 25 1789 2689 3589 3679 4579 4678 12589 12679 13489 13579 13678 14569 14578 23479 23569 23578 24568 34567 123469 123478 123568 124567 25 26 2789 3689 4589 4679 5678 12689 13589 13679 14579 14678 23489 23579 23678 24569 24578 34568 123479 123569 123578 124568 134567 26 27 3789 4689 5679 12789 13689 14589 14679 15678 23589 23679 24579 24678 34569 34578 123489 123579 123678 124569 124578 134568 234567 27 28 4789 5689 13789 14689 15679 23689 24589 24679 25678 34579 34678 123589 123679 124579 124678 134569 134578 234568 1234567 28 29 5789 14789 15689 23789 24689 25679 34589 34679 35678 123689 124589 124679 125678 134579 134678 234569 234578 1234568 29 30 6789 15789 24789 25689 34689 35679 45678 123789 124689 125679 134589 134679 135678 234579 234678 1234569 1234578 30 31 16789 25789 34789 35689 45679 124789 125689 134689 135679 145678 234589 234679 235678 1234579 1234678 31 32 26789 35789 45689 125789 134789 135689 145679 234689 235679 245678 1234589 1234679 1235678 32 33 36789 45789 126789 135789 145689 234789 235689 245679 345678 1234689 1235679 1245678 33 34 46789 136789 145789 235789 245689 345679 1234789 1235689 1245679 1345678 34 35 56789 146789 236789 245789 345689 1235789 1245689 1345679 2345678 35 36 156789 246789 345789 1236789 1245789 1345689 2345679 36 37 256789 346789 1246789 1345789 2345689 37 38 356789 1256789 1346789 2345789 38 39 456789 1356789 2346789 39 40 1456789 2356789 40 41 2456789 41 42 3456789 42

Fig. 2  Killer Combination Table

Look for a workable list of combinations for cages. From Fig. 2, the coloured shaded areas represent:

 Shade Colour Cells per cage Yellow 2 Green 3 Blue 4 Orange 5 Tan 6 Grey 7

... look for the 'low hanging fruit'  - the easy 'one choice' combinations:
3(2): 12
4(2): 13
16(2): 79
17(2): 89

6(3): 123   ==> Cage sum of 6 in 3 cells: since there can't be repeated #s, the only combination is 1-2-3...
7(3): 124
23(3): 689
24(3): 789

10(4): 1234
11(4): 1235
29(4): 5789
30(4): 6789

15(5): 12345
16(5): 12346
34(5): 46789
35(5): 56789

21(6): 123456
22(6): 123457
38(6): 356789
39(6): 456789

Be careful not to get too hung up on analyzing every possible combination - only resort to using combinations once you've exhausted other solution techniques. Unfortunately, the Killer Sudoku in Fig. 1 doesn't have any of the above 'low hanging fruit' to choose from - guess that's why it's ranked as a Diabolical Killer Sudoku - enough to whet your appetite even further!

Looking for a World-1st combination of Sudoku and Killer Sudoku? Try kSudoku...

Fig. 3  kSudoku... easy Killer Sudoku

Killer Sudoku Puzzles @ suJoku.com

# Jigsaw Sudoku Rules

For standard 9x9 grids: As with standard Sudoku, every row and column must contain the numbers from 1 through 9 once and once only. Unlike standard Sudoku, the contents of each 3x3 block do not need to contain the numbers 1 - 9 only. You will notice the grid is split into several different shapes: each of these shapes must contain the numbers from 1 - 9 exactly once, and these pieces join together to make up the Sudoku puzzle, hence the name 'Jigsaw' Sudoku. Unlike Killer Sudoku, you don't need to know the sum for each 'cage' since each cage must sum up to 45 (since 1 to 9 are unique in a Jigsaw Sudoku 'cage').

The aim of the puzzle is as per normal Sudoku: you must complete the grid so as to satisfy the rules above, using logic alone: there is no need to guess.
All our Jigsaw Sudoku puzzles are symmetrical and have one unique solution.

October 2010
Cheers!
Joe Defries
the joe in joe-ks.com & suJoku.com