Killer Sudoku Lingo

(mirrored from http://www.djape.net/sudoku/forum/viewtopic.php?t=280)

On behalf of Shai, here is the summarized Killer Sudoku Lingo.

This makes the previous thread on the same topic obsolete. Any comments and updates should be posted in this thread.

Killer Sudoku Lingo

Cell combinations:

rxcy or RxCy, while x,y are numbers in the range {1..9}, means the cell in row x, column y. Counting goes from top to bottom, and from left to right. r1c1=1 (or "r1c1 is 1") means there's a 1 in r1c1. r1c1/2 means combining the cells of r1c1 and r1c2. r1/2c1 means r1c1 & r2c1. r1c1/2/3 means r1c1, r1c2 & r1c3. r1c1/2/4 means r1c1, r1c2 & r1c4. r1c1/2=7 means r1c1+r1c2=7. r1/2c1/2 means the r1c1, r1c2, r2c1 & r2c2. Also: not using the "/"s. "r1c125" is the same as "r1c1/2/5".

Nonet

A 3 X 3 square, in which all digits have to appear. There are 9 nonets in each sudoku, and they are numbered, for the sake of conversation:

1 2 3
4 5 6
7 8 9

So "nonet 1" is the top-left nonet, etc. Also: Nx means nonet x (N1, N2,..) Also: "Block" or "Box" instead of "Nonet".

Cage

A few cells grouped together, usually with a closed dotted line. The sum of the digits in these cells is given/known. A digit can't appear twice in a cage, even if it's possible accroding to other sudoku rules.

x-cage

A cage whose sum is x. Ex: "The 16-cage in nonet 2 is {9,7}".

x/y or x/y-cage

An x-cage of y cells. Ex: 16/3 means a 16-cage of 3 cells, 20/5-cage means a cage of 5 cells whose sum is 20, etc. Also: x(y)-cage is the same. Ex: "11(2)-cage" is the same as "11/2-cage".

{A1,A2,..,An}

The set of numbers A1,..,An. Order is unknown or irrelevant. Ex: "r1c1/2={2,4}" means that either r1c1=2 & r1c2=4 or that r1c1=4 & r1c2=2. Also: not using commas. "{123}" is the same as "{1,2,3}".

[A1,A2,..,An]

The ordered set of numbers A1,..,An. The order goes from left to right, or from top to bottom. fEx: "r1c1/2=[2,4]" means that r1c1=2 & r1c2=4. Ex: "r4/5c7=[4,5]" means that r4c7=4 & r5c7=5. Improvement: If there's a cage who's not in the shape of 1 X n or n X 1, The order goes first from left to right and only then from top to bottom. Ex: A 23/4-cage in cells r1c1, r1c2, r2c1 & r2c2. Saying that "The 23/4-cage in nonet 1 is [8,7,6,2]" means r1c1=8, r1c2=7, r2c1=6, r2c2=2. Also: not using commas.

45-rule:

"45" on R/N/Cx -> conclusion Ex: "45" on N1 -> r3c3=1, means that appying the 45-rule on nonet 1 reveals that r3c3=1. Ex: "45" on C4 -> r4/5/8c4=8, means that applying the 45-rule on column 4 reveals that r4c4+r5c4+r8c4=8. Ex: "45" on R6-9 -> r5c1=9, means that applying the 45-rule on the 4 bottom rows reveals that r5c1 is 9. Ex: "45" on N124 -> r5c3=4, means that appying the 45-rule on nonets 1,2 & 4 reveals that r5c3 is 4. Comment: The 45-rule says that since each row column and noent contain all the digits {1,..,9} then the sum of the digits in each row, column and nonet is 45. Also: R6..9 is the same as R6-9

Arrow:

Fact -> Conclusion.

Ex: "16/2 in N1 is {9,7} -> 12-cage in N1 is {8,4}". Ex: Fact -> conclusion 1 & conclusion 2. Ex: Fact -> Conclusion 1, Conclusion 2,... Ex: Fact -> conclusion -> new conclusion,... Ex: Fact1 & Fact 2 -> conclusion. Ex: Action on Target -> conclusion (45 rule, Substraction Combo..) Also: Reversed arrow "<-", means "becasue". Ex: "6(2) in N1 = {2,4} (<- 7(2) in N1 = {1,6})".

Not:

~x means not x

Ex: "r1c1 = ~4" means the digit in r1c1 is not 4. Ex: "r1c1/2/3 = ~3" means that there's no 3 in r1c1/2/3. Ex: "r1c1 = ~246" means that r1c1 is not 2, 4 or 6. Ex: "r1c1/2/3 = ~246" means that there's no 2, 4, or 6, in r1c1/2/3 Ex: "r1c1/2/3 = ~{2,4,6}" means that r1c1/2/3 is not {2,4,6}. Ex: "r1c1/2 = ~[1,7] means that r1c1/2 is not [1,7]. Ex: "r1c1/2 =~{3,6|4,5}" means that r1c1/2 is not {3,6} nor {4,5}. Ex: "r1c1/2/3 = ~39 means that there is no 3 or 9 in r1c1/2/3 Ex: "r1c1/2/3 = ~{3,9} means that 3 and 9 can't be both in r1c1/2/3

Bigger / Smaller:

<, >, <=, >= Ex: "r1c1 < 7" means that the digit in r1c1 is smaller than 7. Ex: "r1c1/2 > 10" means that the sum of the digits in r1c1 & r1c2 is bigger than 10. Ex: "Cells in r1c1/2 <= 7" means that each digit in r1c1 & r1c2 is at most 7. Also: "Digits in r1c1/2 >= 5", same as cells. Also: "Each" instead of "Cells" or "Digits". Note: some forums/web-pages don't suppot the GREATER/SMALLER characters.

Or & Must:

Option 1 | Option 2 |..... Ex: "r1c1 = 1|2", means that the digit in r1c1 is either 1 or 2. Also: "r1c1 = 1 or 2". Ex: "r1c1 = 1|2|7" means that the digit in r1c1 is 1,2 or 7. Ex: "r1c1/2 = {2,4}|{1,5}" means that r1c1/2 is {2,4} or {1,5}. Ex: "r1c1/2 = {24|15}" means the same. Ex: "r1c1/2 = {2,4}|[1,5]" means that r1c1/2 is {2,4} or [1,5]. Ex: "r1c1/2 = {(24)|[15]}" means the same. Ex: "r1c1 = {1,2}" means that the digit in r1c1 is either 1 or 2. Ex: "r1c1/2 = {1,2,3}" means that the digits in r1c1/2 are from the set {1,2,3}. Ex: "r1c1/2 = {(1)23}" means that there's 1 in r1c1/2 and the other digit is 2 or 3 (The "must numbers" are in parentheses, and the rest are from what's left). Ex: "r1c1/2 = {(2|3)1}" means the same, There's 1 and either 2 or 3 in r1c1/2 (The "optionals" are in parentheses, and the "must numbers" are what's left). Comment: Although the last two seem contraditory, there hasn't been an agreement on the subject in the Killer-Sudoku community, and both are widely used, and understood. Ex: "r1c1/2/3/4 = {(98)4321}" means that there must be 9 & 8 in r1c1/2/3/4 and the other two digits are from the set {1,2,3,4}. Ex: "r1c1/2/3/4 = {(14|23|13)98}" means that there must be 9 & 8 in r1c1/2/3/4 and the other two digits are {1,4}, {2,3} or {1,3}. Ex: "r1c1/2 = [24|15]" means that r1c1/2 is [2,4] or [1,5]. Ex: "r1c1/2 = {(1|2)(3|4)}" means that r1c1 must contain 1 or 2, as well as 3 or 4. Same as {13|14|23|24} Ex: "r1c1/2/3 = {(1|2)(27|36|45|35)}" means that r1c1/2/3 must contain 1 or 2, as well as {27}, {36}, {45} or {35}. Ex: "r1c1/2/3 = {(1|2)...}" means that r1c1/2/3 must contain 1 or 2, (and the rest is unknown/irrelevant).

Perspectives and ways to look at the puzzle:

Rx:, Cx:, Nx: Ex: "R1: 1 in r1c9" means that looking at row 1 shows that the 1 in that row is in r1c9 Ex: "R1: 3 can only go in C7-9" means that looking in row 1 shows that in R1, 3 can only go at r1c7/8/9. Ex: "C1: 1 in 8-cage" means that looking at column 1 shows that the 1 in that column must be in the 8-cage. Ex: "N1: {79} in R2" means that looking at Nonet 1 shows that the 7 and 9 in that nonet must be in row 2.

Contradiction:

con. Ex: "If r1c1=5 then r1c2=3, but r1c2 is part of a 6(2)-cage, con".

In: Digit/Set in Group. Ex: "5 in 14-cage in N1" means there must be a 5 in the 14-cage in nonet 1. Ex: "5 in r1c1/2/3" means there must be a 5 in r1c1/2/3. Ex: "{1,2} in 14/4" means there must be 1 & 2 in the 14(4)-cage. Ex: "{1,2} in r1c1/2/3" means there must be 1 & 2 in r1c1/2/3.

Ranges:

.. (for cells,rows,columns or nonets) {x..y} (for cell values) (x..y) (for sums) Ex: "R1..3" means the three top rows. Ex: "r1c4..7" means r1c4/5/6/7. Ex: "r1c1/2/3={4..6}" means that r1c1/2/3 contains the digits 4 to 6 - {4,5,6}. Ex: "r1c1/2 = {1..4}" means that r1c1/2 contains digits from the set {1,2,3,4}. Ex: "r1c1/2 = (13..15)" means that the sum of r1c1 and r1c2 is 13, 14 or 15. Ex: "r1c1/2 = (9|11|13..15)" means that the sum of r1c1/2 is 9, 11, 13, 14 or 15.

Substraction Combo:

SC on Target -> conclusion. Ex: "SC on 14/3 in N1 -> r1c1/2={3,6}" means that substraction combo on the 14/3 cage in N1 shows that r1c1/2 = {3,6}. Comment: Substraction Combo is a method to find possible combinations using substraction. For example, if we know there's a 14(3)-cage in r1c1, r1c2, r2c1, and we know that r2c1=5, and that r1c1/2/3={3,6,8} "SC on 14/3 in N1 -> r1c1/2={3,6}" means that since r2c1=5 and 14-5=9, then r1c1+r1c2=9, and the only possibility to get a sum of 9 from two digits in the set {3,6,8} is 3 & 6, so r1c1/2={3,6}.

Hidden-Cages:

H-x-cage x-cage-H Ex: "The H-6-cage in N1 = {2,4}" means that the hidden 6-cage in N1 is {2,4}. Ex: "H-13(3) in R1 = {1,4,8}" means that the hidden 13(3)-cage in N1 is {1,4,8}. Ex: "5-cage-H in C1 = {2,3}" means that the hidden 5-cage in C1 is {2,3}. Comment: A hidden cage, is a cage that is not drawn in the puzzle, but implied by the current solving position, and for all purposes "acts" like a normal cage (i.e. fixed sum, and no repetitions of digits). Ex: If we know that r1c1 + r1c4 + r1c9 = 13 (by using the 45-rule, for example), then we can say that r1c1/4/9 is a hidden 13-cage. On the other hand, if we know that r3c1 + r1c9 = 6, we can't say for certain that r3c1 & r1c9 is a hidden 6(2)-cage, becasue they both can contain a 3.

Naked:

Naked single, Naked pair, Naked triplet.... Ex: "r1c1=1, naked single in R1" means that the only place for 1 in R1 is r1c1. Ex: "r1c1/2={34}, naked pair in N1" means that the only places for 3 & 4 in N1 are in r1c1 & r1c2. Ex: "r1c1/5/9 = {123}, naked triplet in R1" means that the only places for 1,2 & 3 in R1 are in r1c1, r1c5 & r1c9. Also: "Pinned cell" instead of "naked single".

Innies & Outies:

Cells which are inside, or outside, a given row(s), column(s), or nonet(s), whose values or sum-of-values, can be known using the 45-rule. Ex: "r1c1=1, innie of R1" means that using the 45-rule on R1 shows that r1c1=1. Ex: "r2c1=1, outie of R1" means that using the 45-rule on R1 shows that r2c1=1. Ex: "r4c1/2=12, outies of N1" means that using the 45-rule on N1 shows that r4c1+r4c2=12. Ex: "r1/4/8c3=24", outies of C12" means that using the 45-rule on columns 1 & 2 shows that r1c3+r4c3+r8c3=24. Ex" "r1c1+r3c6=17, innies of N12" means that using the 45-rule on nonets 1 & 2 shows that r1c1+r3c6=17. Ex: "r6c1+r4c8/9=16", outies of N7" means that using the 45-rule on N7 shows that r6c1+r4c8+r4c9=16.

Buddies:

The buddies of a cell, are all the cells which are in the same nonet, row, column or cage (and therefore must contain a different digit).