Do digits repeat inside a killer cage?

No. A digit can appear at most once per cage, on top of the usual row, column, and box constraints.

What is the 45 rule in killer sudoku?

Each row, column, and box contains 1–9, which sums to 45. Comparing cage totals against 45 lets you deduce leftover cells.

Which killer sudoku cages have only one possible combination?

Sixteen of them. For each cage size, the two smallest and two largest sums are forced: 3 and 4 (and 16, 17) in a two-cell cage, 6 and 7 (and 23, 24) in a three-cell cage, 10 and 11 (and 29, 30) in a four-cell cage, and 15 and 16 (and 34, 35) in a five-cell cage.

How do you play killer sudoku?

Fill the grid so every row, column and 3x3 box holds 1-9 exactly once, and every dotted cage adds up to its printed total without repeating a digit inside the cage. Killer grids usually start with few or no given digits - the cage sums are the clues.

Is killer sudoku harder than normal sudoku?

It adds an arithmetic layer, but the cage sums also give extra information — many solvers find well-set killers more satisfying than classic grids.

Killer Sudoku: Rules & How to Solve

Cages with target sums turn classic sudoku into an arithmetic puzzle. Here's the rule and the techniques that crack it.

The rule

Digits inside a dotted cage must add up to the small number printed in its top-left corner, and a digit can't repeat within a single cage. Normal sudoku rules still apply: 1–9 once per row, column, and box.

How to solve killer sudoku

The 45 rule

Every row, column, and 3×3 box totals 45. If cages cover a box and spill out by one cell, you can solve that cell by subtracting the cage sums from 45.

Lock small cages first

A two-cell cage summing to 3 can only be {1,2}; a sum of 17 can only be {8,9}. These "killer pairs" eliminate candidates from the whole row, column, or box.

No repeats inside a cage

Even when several combinations fit a sum, the no-repeat rule often rules most of them out — a 3-cell cage of 7 is {1,2,4}, never {1,3,3}.

Killer sudoku cage combinations

Most of killer solving is pattern recall: seeing 17 in a two-cell cage and knowing instantly it is {8,9}. The tables below list every cage sum from two to five cells and the digit sets that can produce it. Rows marked with a dot have exactly one combination — those are the cages to fill first.

The cages that solve themselves

Sixteen sums across all cage sizes admit only one set of digits. Learn these and you will always have an opening move:

2 cells: 3=12 · 4=13 · 16=79 · 17=89
3 cells: 6=123 · 7=124 · 23=689 · 24=789
4 cells: 10=1234 · 11=1235 · 29=5789 · 30=6789
5 cells: 15=12345 · 16=12346 · 34=46789 · 35=56789

The pattern is symmetric: the two lowest and two highest sums of every cage size are always unique, because there is only one way to pack the smallest — or largest — available digits.

2-cell cages

Every 2-cell cage sum and the digit sets that make it.
Sum	Possible combinations
3	`12`
4	`13`
5	`14` `23`
6	`15` `24`
7	`16` `25` `34`
8	`17` `26` `35`
9	`18` `27` `36` `45`
10	`19` `28` `37` `46`
11	`29` `38` `47` `56`
12	`39` `48` `57`
13	`49` `58` `67`
14	`59` `68`
15	`69` `78`
16	`79`
17	`89`

3-cell cages

Every 3-cell cage sum and the digit sets that make it.
Sum	Possible combinations
6	`123`
7	`124`
8	`125` `134`
9	`126` `135` `234`
10	`127` `136` `145` `235`
11	`128` `137` `146` `236` `245`
12	`129` `138` `147` `156` `237` `246` `345`
13	`139` `148` `157` `238` `247` `256` `346`
14	`149` `158` `167` `239` `248` `257` `347` `356`
15	`159` `168` `249` `258` `267` `348` `357` `456`
16	`169` `178` `259` `268` `349` `358` `367` `457`
17	`179` `269` `278` `359` `368` `458` `467`
18	`189` `279` `369` `378` `459` `468` `567`
19	`289` `379` `469` `478` `568`
20	`389` `479` `569` `578`
21	`489` `579` `678`
22	`589` `679`
23	`689`
24	`789`

4-cell cages

Every 4-cell cage sum and the digit sets that make it.
Sum	Possible combinations
10	`1234`
11	`1235`
12	`1236` `1245`
13	`1237` `1246` `1345`
14	`1238` `1247` `1256` `1346` `2345`
15	`1239` `1248` `1257` `1347` `1356` `2346`
16	`1249` `1258` `1267` `1348` `1357` `1456` `2347` `2356`
17	`1259` `1268` `1349` `1358` `1367` `1457` `2348` `2357` `2456`
18	`1269` `1278` `1359` `1368` `1458` `1467` `2349` `2358` `2367` `2457` `3456`
19	`1279` `1369` `1378` `1459` `1468` `1567` `2359` `2368` `2458` `2467` `3457`
20	`1289` `1379` `1469` `1478` `1568` `2369` `2378` `2459` `2468` `2567` `3458` `3467`
21	`1389` `1479` `1569` `1578` `2379` `2469` `2478` `2568` `3459` `3468` `3567`
22	`1489` `1579` `1678` `2389` `2479` `2569` `2578` `3469` `3478` `3568` `4567`
23	`1589` `1679` `2489` `2579` `2678` `3479` `3569` `3578` `4568`
24	`1689` `2589` `2679` `3489` `3579` `3678` `4569` `4578`
25	`1789` `2689` `3589` `3679` `4579` `4678`
26	`2789` `3689` `4589` `4679` `5678`
27	`3789` `4689` `5679`
28	`4789` `5689`
29	`5789`
30	`6789`

5-cell cages

Every 5-cell cage sum and the digit sets that make it.
Sum	Possible combinations
15	`12345`
16	`12346`
17	`12347` `12356`
18	`12348` `12357` `12456`
19	`12349` `12358` `12367` `12457` `13456`
20	`12359` `12368` `12458` `12467` `13457` `23456`
21	`12369` `12378` `12459` `12468` `12567` `13458` `13467` `23457`
22	`12379` `12469` `12478` `12568` `13459` `13468` `13567` `23458` `23467`
23	`12389` `12479` `12569` `12578` `13469` `13478` `13568` `14567` `23459` `23468` `23567`
24	`12489` `12579` `12678` `13479` `13569` `13578` `14568` `23469` `23478` `23568` `24567`
25	`12589` `12679` `13489` `13579` `13678` `14569` `14578` `23479` `23569` `23578` `24568` `34567`
26	`12689` `13589` `13679` `14579` `14678` `23489` `23579` `23678` `24569` `24578` `34568`
27	`12789` `13689` `14589` `14679` `15678` `23589` `23679` `24579` `24678` `34569` `34578`
28	`13789` `14689` `15679` `23689` `24589` `24679` `25678` `34579` `34678`
29	`14789` `15689` `23789` `24689` `25679` `34589` `34679` `35678`
30	`15789` `24789` `25689` `34689` `35679` `45678`
31	`16789` `25789` `34789` `35689` `45679`
32	`26789` `35789` `45689`
33	`36789` `45789`
34	`46789`
35	`56789`

Cages of six cells or more are easiest to read backwards: a 6-cell cage summing to S uses the same digits as a 3-cell cage summing to 45 − S, just inverted. The same trick turns a 7-cell cage into a 2-cell lookup.

Frequently asked questions

Do digits repeat inside a killer cage?: No. A digit can appear at most once per cage, on top of the usual row, column, and box constraints.
What is the 45 rule in killer sudoku?: Each row, column, and box contains 1–9, which sums to 45. Comparing cage totals against 45 lets you deduce leftover cells.
Which killer sudoku cages have only one possible combination?: Sixteen of them. For each cage size, the two smallest and two largest sums are forced: 3 and 4 (and 16, 17) in a two-cell cage, 6 and 7 (and 23, 24) in a three-cell cage, 10 and 11 (and 29, 30) in a four-cell cage, and 15 and 16 (and 34, 35) in a five-cell cage.
How do you play killer sudoku?: Fill the grid so every row, column and 3×3 box holds 1–9 exactly once, and every dotted cage adds up to its printed total without repeating a digit inside the cage. Killer grids usually start with few or no given digits — the cage sums are the clues.
Is killer sudoku harder than normal sudoku?: It adds an arithmetic layer, but the cage sums also give extra information — many solvers find well-set killers more satisfying than classic grids.

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