KenKen Puzzles

7×7 Cage Combinations

All valid digit combinations for 7×7 KenKen cages using digits 1–7.

Digits available: 1–7 • Max cage size: 4 cells

+ Addition − Subtraction × Multiplication ÷ Division

+ Addition

2-Cell Cages

Target Possible Combinations Count
2+
1, 1
1
3+
1, 2
1
4+
1, 3 2, 2
2
5+
1, 4 2, 3
2
6+
1, 5 2, 4 3, 3
3
7+
1, 6 2, 5 3, 4
3
8+
1, 7 2, 6 3, 5 4, 4
4
9+
2, 7 3, 6 4, 5
3
10+
3, 7 4, 6 5, 5
3
11+
4, 7 5, 6
2
12+
5, 7 6, 6
2
13+
6, 7
1
14+
7, 7
1

3-Cell Cages

Target Possible Combinations Count
3+
1, 1, 1
1
4+
1, 1, 2
1
5+
1, 1, 3 1, 2, 2
2
6+
1, 1, 4 1, 2, 3 2, 2, 2
3
7+
1, 1, 5 1, 2, 4 1, 3, 3 2, 2, 3
4
8+
1, 1, 6 1, 2, 5 1, 3, 4 2, 2, 4 2, 3, 3
5
9+
1, 1, 7 1, 2, 6 1, 3, 5 1, 4, 4 2, 2, 5 2, 3, 4 3, 3, 3
7
10+
1, 2, 7 1, 3, 6 1, 4, 5 2, 2, 6 2, 3, 5 2, 4, 4 3, 3, 4
7
11+
1, 3, 7 1, 4, 6 1, 5, 5 2, 2, 7 2, 3, 6 2, 4, 5 3, 3, 5 3, 4, 4
8
12+
1, 4, 7 1, 5, 6 2, 3, 7 2, 4, 6 2, 5, 5 3, 3, 6 3, 4, 5 4, 4, 4
8
13+
1, 5, 7 1, 6, 6 2, 4, 7 2, 5, 6 3, 3, 7 3, 4, 6 3, 5, 5 4, 4, 5
8
14+
1, 6, 7 2, 5, 7 2, 6, 6 3, 4, 7 3, 5, 6 4, 4, 6 4, 5, 5
7
15+
1, 7, 7 2, 6, 7 3, 5, 7 3, 6, 6 4, 4, 7 4, 5, 6 5, 5, 5
7
16+
2, 7, 7 3, 6, 7 4, 5, 7 4, 6, 6 5, 5, 6
5
17+
3, 7, 7 4, 6, 7 5, 5, 7 5, 6, 6
4
18+
4, 7, 7 5, 6, 7 6, 6, 6
3
19+
5, 7, 7 6, 6, 7
2
20+
6, 7, 7
1
21+
7, 7, 7
1

4-Cell Cages

Target Possible Combinations Count
4+
1, 1, 1, 1
1
5+
1, 1, 1, 2
1
6+
1, 1, 1, 3 1, 1, 2, 2
2
7+
1, 1, 1, 4 1, 1, 2, 3 1, 2, 2, 2
3
8+
1, 1, 1, 5 1, 1, 2, 4 1, 1, 3, 3 1, 2, 2, 3 2, 2, 2, 2
5
9+
1, 1, 1, 6 1, 1, 2, 5 1, 1, 3, 4 1, 2, 2, 4 1, 2, 3, 3 2, 2, 2, 3
6
10+
1, 1, 1, 7 1, 1, 2, 6 1, 1, 3, 5 1, 1, 4, 4 1, 2, 2, 5 1, 2, 3, 4 1, 3, 3, 3 2, 2, 2, 4 2, 2, 3, 3
9
11+
1, 1, 2, 7 1, 1, 3, 6 1, 1, 4, 5 1, 2, 2, 6 1, 2, 3, 5 1, 2, 4, 4 1, 3, 3, 4 2, 2, 2, 5 2, 2, 3, 4 2, 3, 3, 3
10
12+
1, 1, 3, 7 1, 1, 4, 6 1, 1, 5, 5 1, 2, 2, 7 1, 2, 3, 6 1, 2, 4, 5 1, 3, 3, 5 1, 3, 4, 4 2, 2, 2, 6 2, 2, 3, 5 2, 2, 4, 4 2, 3, 3, 4 3, 3, 3, 3
13
13+
1, 1, 4, 7 1, 1, 5, 6 1, 2, 3, 7 1, 2, 4, 6 1, 2, 5, 5 1, 3, 3, 6 1, 3, 4, 5 1, 4, 4, 4 2, 2, 2, 7 2, 2, 3, 6 2, 2, 4, 5 2, 3, 3, 5 2, 3, 4, 4 3, 3, 3, 4
14
14+
1, 1, 5, 7 1, 1, 6, 6 1, 2, 4, 7 1, 2, 5, 6 1, 3, 3, 7 1, 3, 4, 6 1, 3, 5, 5 1, 4, 4, 5 2, 2, 3, 7 2, 2, 4, 6 2, 2, 5, 5 2, 3, 3, 6 2, 3, 4, 5 2, 4, 4, 4 3, 3, 3, 5 3, 3, 4, 4
16
15+
1, 1, 6, 7 1, 2, 5, 7 1, 2, 6, 6 1, 3, 4, 7 1, 3, 5, 6 1, 4, 4, 6 1, 4, 5, 5 2, 2, 4, 7 2, 2, 5, 6 2, 3, 3, 7 2, 3, 4, 6 2, 3, 5, 5 2, 4, 4, 5 3, 3, 3, 6 3, 3, 4, 5 3, 4, 4, 4
16
16+
1, 1, 7, 7 1, 2, 6, 7 1, 3, 5, 7 1, 3, 6, 6 1, 4, 4, 7 1, 4, 5, 6 1, 5, 5, 5 2, 2, 5, 7 2, 2, 6, 6 2, 3, 4, 7 2, 3, 5, 6 2, 4, 4, 6 2, 4, 5, 5 3, 3, 3, 7 3, 3, 4, 6 3, 3, 5, 5 3, 4, 4, 5 4, 4, 4, 4
18
17+
1, 2, 7, 7 1, 3, 6, 7 1, 4, 5, 7 1, 4, 6, 6 1, 5, 5, 6 2, 2, 6, 7 2, 3, 5, 7 2, 3, 6, 6 2, 4, 4, 7 2, 4, 5, 6 2, 5, 5, 5 3, 3, 4, 7 3, 3, 5, 6 3, 4, 4, 6 3, 4, 5, 5 4, 4, 4, 5
16
18+
1, 3, 7, 7 1, 4, 6, 7 1, 5, 5, 7 1, 5, 6, 6 2, 2, 7, 7 2, 3, 6, 7 2, 4, 5, 7 2, 4, 6, 6 2, 5, 5, 6 3, 3, 5, 7 3, 3, 6, 6 3, 4, 4, 7 3, 4, 5, 6 3, 5, 5, 5 4, 4, 4, 6 4, 4, 5, 5
16
19+
1, 4, 7, 7 1, 5, 6, 7 1, 6, 6, 6 2, 3, 7, 7 2, 4, 6, 7 2, 5, 5, 7 2, 5, 6, 6 3, 3, 6, 7 3, 4, 5, 7 3, 4, 6, 6 3, 5, 5, 6 4, 4, 4, 7 4, 4, 5, 6 4, 5, 5, 5
14
20+
1, 5, 7, 7 1, 6, 6, 7 2, 4, 7, 7 2, 5, 6, 7 2, 6, 6, 6 3, 3, 7, 7 3, 4, 6, 7 3, 5, 5, 7 3, 5, 6, 6 4, 4, 5, 7 4, 4, 6, 6 4, 5, 5, 6 5, 5, 5, 5
13
21+
1, 6, 7, 7 2, 5, 7, 7 2, 6, 6, 7 3, 4, 7, 7 3, 5, 6, 7 3, 6, 6, 6 4, 4, 6, 7 4, 5, 5, 7 4, 5, 6, 6 5, 5, 5, 6
10
22+
1, 7, 7, 7 2, 6, 7, 7 3, 5, 7, 7 3, 6, 6, 7 4, 4, 7, 7 4, 5, 6, 7 4, 6, 6, 6 5, 5, 5, 7 5, 5, 6, 6
9
23+
2, 7, 7, 7 3, 6, 7, 7 4, 5, 7, 7 4, 6, 6, 7 5, 5, 6, 7 5, 6, 6, 6
6
24+
3, 7, 7, 7 4, 6, 7, 7 5, 5, 7, 7 5, 6, 6, 7 6, 6, 6, 6
5
25+
4, 7, 7, 7 5, 6, 7, 7 6, 6, 6, 7
3
26+
5, 7, 7, 7 6, 6, 7, 7
2
27+
6, 7, 7, 7
1
28+
7, 7, 7, 7
1

− Subtraction

2-Cell Cages

Target Possible Combinations Count
1−
1, 2 2, 3 3, 4 4, 5 5, 6 6, 7
6
2−
1, 3 2, 4 3, 5 4, 6 5, 7
5
3−
1, 4 2, 5 3, 6 4, 7
4
4−
1, 5 2, 6 3, 7
3
5−
1, 6 2, 7
2
6−
1, 7
1

× Multiplication

2-Cell Cages

Target Possible Combinations Count
1×
1, 1
1
2×
1, 2
1
3×
1, 3
1
4×
1, 4 2, 2
2
5×
1, 5
1
6×
1, 6 2, 3
2
7×
1, 7
1
8×
2, 4
1
9×
3, 3
1
10×
2, 5
1
12×
2, 6 3, 4
2
14×
2, 7
1
15×
3, 5
1
16×
4, 4
1
18×
3, 6
1
20×
4, 5
1
21×
3, 7
1
24×
4, 6
1
25×
5, 5
1
28×
4, 7
1
30×
5, 6
1
35×
5, 7
1
36×
6, 6
1
42×
6, 7
1
49×
7, 7
1

3-Cell Cages

Target Possible Combinations Count
1×
1, 1, 1
1
2×
1, 1, 2
1
3×
1, 1, 3
1
4×
1, 1, 4 1, 2, 2
2
5×
1, 1, 5
1
6×
1, 1, 6 1, 2, 3
2
7×
1, 1, 7
1
8×
1, 2, 4 2, 2, 2
2
9×
1, 3, 3
1
10×
1, 2, 5
1
12×
1, 2, 6 1, 3, 4 2, 2, 3
3
14×
1, 2, 7
1
15×
1, 3, 5
1
16×
1, 4, 4 2, 2, 4
2
18×
1, 3, 6 2, 3, 3
2
20×
1, 4, 5 2, 2, 5
2
21×
1, 3, 7
1
24×
1, 4, 6 2, 2, 6 2, 3, 4
3
25×
1, 5, 5
1
27×
3, 3, 3
1
28×
1, 4, 7 2, 2, 7
2
30×
1, 5, 6 2, 3, 5
2
32×
2, 4, 4
1
35×
1, 5, 7
1
36×
1, 6, 6 2, 3, 6 3, 3, 4
3
40×
2, 4, 5
1
42×
1, 6, 7 2, 3, 7
2
45×
3, 3, 5
1
48×
2, 4, 6 3, 4, 4
2
49×
1, 7, 7
1
50×
2, 5, 5
1
54×
3, 3, 6
1
56×
2, 4, 7
1
60×
2, 5, 6 3, 4, 5
2
63×
3, 3, 7
1
64×
4, 4, 4
1
70×
2, 5, 7
1
72×
2, 6, 6 3, 4, 6
2
75×
3, 5, 5
1
80×
4, 4, 5
1
84×
2, 6, 7 3, 4, 7
2
90×
3, 5, 6
1
96×
4, 4, 6
1
98×
2, 7, 7
1
100×
4, 5, 5
1
105×
3, 5, 7
1
108×
3, 6, 6
1
112×
4, 4, 7
1
120×
4, 5, 6
1
125×
5, 5, 5
1
126×
3, 6, 7
1
140×
4, 5, 7
1
144×
4, 6, 6
1
147×
3, 7, 7
1
150×
5, 5, 6
1
168×
4, 6, 7
1
175×
5, 5, 7
1
180×
5, 6, 6
1
196×
4, 7, 7
1
210×
5, 6, 7
1
216×
6, 6, 6
1
245×
5, 7, 7
1
252×
6, 6, 7
1
294×
6, 7, 7
1
343×
7, 7, 7
1

4-Cell Cages

Target Possible Combinations Count
1×
1, 1, 1, 1
1
2×
1, 1, 1, 2
1
3×
1, 1, 1, 3
1
4×
1, 1, 1, 4 1, 1, 2, 2
2
5×
1, 1, 1, 5
1
6×
1, 1, 1, 6 1, 1, 2, 3
2
7×
1, 1, 1, 7
1
8×
1, 1, 2, 4 1, 2, 2, 2
2
9×
1, 1, 3, 3
1
10×
1, 1, 2, 5
1
12×
1, 1, 2, 6 1, 1, 3, 4 1, 2, 2, 3
3
14×
1, 1, 2, 7
1
15×
1, 1, 3, 5
1
16×
1, 1, 4, 4 1, 2, 2, 4 2, 2, 2, 2
3
18×
1, 1, 3, 6 1, 2, 3, 3
2
20×
1, 1, 4, 5 1, 2, 2, 5
2
21×
1, 1, 3, 7
1
24×
1, 1, 4, 6 1, 2, 2, 6 1, 2, 3, 4 2, 2, 2, 3
4
25×
1, 1, 5, 5
1
27×
1, 3, 3, 3
1
28×
1, 1, 4, 7 1, 2, 2, 7
2
30×
1, 1, 5, 6 1, 2, 3, 5
2
32×
1, 2, 4, 4 2, 2, 2, 4
2
35×
1, 1, 5, 7
1
36×
1, 1, 6, 6 1, 2, 3, 6 1, 3, 3, 4 2, 2, 3, 3
4
40×
1, 2, 4, 5 2, 2, 2, 5
2
42×
1, 1, 6, 7 1, 2, 3, 7
2
45×
1, 3, 3, 5
1
48×
1, 2, 4, 6 1, 3, 4, 4 2, 2, 2, 6 2, 2, 3, 4
4
49×
1, 1, 7, 7
1
50×
1, 2, 5, 5
1
54×
1, 3, 3, 6 2, 3, 3, 3
2
56×
1, 2, 4, 7 2, 2, 2, 7
2
60×
1, 2, 5, 6 1, 3, 4, 5 2, 2, 3, 5
3
63×
1, 3, 3, 7
1
64×
1, 4, 4, 4 2, 2, 4, 4
2
70×
1, 2, 5, 7
1
72×
1, 2, 6, 6 1, 3, 4, 6 2, 2, 3, 6 2, 3, 3, 4
4
75×
1, 3, 5, 5
1
80×
1, 4, 4, 5 2, 2, 4, 5
2
81×
3, 3, 3, 3
1
84×
1, 2, 6, 7 1, 3, 4, 7 2, 2, 3, 7
3
90×
1, 3, 5, 6 2, 3, 3, 5
2
96×
1, 4, 4, 6 2, 2, 4, 6 2, 3, 4, 4
3
98×
1, 2, 7, 7
1
100×
1, 4, 5, 5 2, 2, 5, 5
2
105×
1, 3, 5, 7
1
108×
1, 3, 6, 6 2, 3, 3, 6 3, 3, 3, 4
3
112×
1, 4, 4, 7 2, 2, 4, 7
2
120×
1, 4, 5, 6 2, 2, 5, 6 2, 3, 4, 5
3
125×
1, 5, 5, 5
1
126×
1, 3, 6, 7 2, 3, 3, 7
2
128×
2, 4, 4, 4
1
135×
3, 3, 3, 5
1
140×
1, 4, 5, 7 2, 2, 5, 7
2
144×
1, 4, 6, 6 2, 2, 6, 6 2, 3, 4, 6 3, 3, 4, 4
4
147×
1, 3, 7, 7
1
150×
1, 5, 5, 6 2, 3, 5, 5
2
160×
2, 4, 4, 5
1
162×
3, 3, 3, 6
1
168×
1, 4, 6, 7 2, 2, 6, 7 2, 3, 4, 7
3
175×
1, 5, 5, 7
1
180×
1, 5, 6, 6 2, 3, 5, 6 3, 3, 4, 5
3
189×
3, 3, 3, 7
1
192×
2, 4, 4, 6 3, 4, 4, 4
2
196×
1, 4, 7, 7 2, 2, 7, 7
2
200×
2, 4, 5, 5
1
210×
1, 5, 6, 7 2, 3, 5, 7
2
216×
1, 6, 6, 6 2, 3, 6, 6 3, 3, 4, 6
3
224×
2, 4, 4, 7
1
225×
3, 3, 5, 5
1
240×
2, 4, 5, 6 3, 4, 4, 5
2
245×
1, 5, 7, 7
1
250×
2, 5, 5, 5
1
252×
1, 6, 6, 7 2, 3, 6, 7 3, 3, 4, 7
3
256×
4, 4, 4, 4
1
270×
3, 3, 5, 6
1
280×
2, 4, 5, 7
1
288×
2, 4, 6, 6 3, 4, 4, 6
2
294×
1, 6, 7, 7 2, 3, 7, 7
2
300×
2, 5, 5, 6 3, 4, 5, 5
2
315×
3, 3, 5, 7
1
320×
4, 4, 4, 5
1
324×
3, 3, 6, 6
1
336×
2, 4, 6, 7 3, 4, 4, 7
2
343×
1, 7, 7, 7
1
350×
2, 5, 5, 7
1
360×
2, 5, 6, 6 3, 4, 5, 6
2
375×
3, 5, 5, 5
1
378×
3, 3, 6, 7
1
384×
4, 4, 4, 6
1
392×
2, 4, 7, 7
1
400×
4, 4, 5, 5
1
420×
2, 5, 6, 7 3, 4, 5, 7
2
432×
2, 6, 6, 6 3, 4, 6, 6
2
441×
3, 3, 7, 7
1
448×
4, 4, 4, 7
1
450×
3, 5, 5, 6
1
480×
4, 4, 5, 6
1
490×
2, 5, 7, 7
1
500×
4, 5, 5, 5
1
504×
2, 6, 6, 7 3, 4, 6, 7
2
525×
3, 5, 5, 7
1
540×
3, 5, 6, 6
1
560×
4, 4, 5, 7
1
576×
4, 4, 6, 6
1
588×
2, 6, 7, 7 3, 4, 7, 7
2
600×
4, 5, 5, 6
1
625×
5, 5, 5, 5
1
630×
3, 5, 6, 7
1
648×
3, 6, 6, 6
1
672×
4, 4, 6, 7
1
686×
2, 7, 7, 7
1
700×
4, 5, 5, 7
1
720×
4, 5, 6, 6
1
735×
3, 5, 7, 7
1
750×
5, 5, 5, 6
1
756×
3, 6, 6, 7
1
784×
4, 4, 7, 7
1
840×
4, 5, 6, 7
1
864×
4, 6, 6, 6
1
875×
5, 5, 5, 7
1
882×
3, 6, 7, 7
1
900×
5, 5, 6, 6
1
980×
4, 5, 7, 7
1
1008×
4, 6, 6, 7
1
1029×
3, 7, 7, 7
1
1050×
5, 5, 6, 7
1
1080×
5, 6, 6, 6
1
1176×
4, 6, 7, 7
1
1225×
5, 5, 7, 7
1
1260×
5, 6, 6, 7
1
1296×
6, 6, 6, 6
1
1372×
4, 7, 7, 7
1
1470×
5, 6, 7, 7
1
1512×
6, 6, 6, 7
1
1715×
5, 7, 7, 7
1
1764×
6, 6, 7, 7
1
2058×
6, 7, 7, 7
1
2401×
7, 7, 7, 7
1

÷ Division

2-Cell Cages

Target Possible Combinations Count
2÷
1, 2 2, 4 3, 6
3
3÷
1, 3 2, 6
2
4÷
1, 4
1
5÷
1, 5
1
6÷
1, 6
1
7÷
1, 7
1
All sizes → 7×7 puzzles → Strategies →