KenKen Puzzles

5×5 Cage Combinations

All valid digit combinations for 5×5 KenKen cages using digits 1–5.

Digits available: 1–5 • 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+
2, 5 3, 4
2
8+
3, 5 4, 4
2
9+
4, 5
1
10+
5, 5
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, 2, 5 1, 3, 4 2, 2, 4 2, 3, 3
4
9+
1, 3, 5 1, 4, 4 2, 2, 5 2, 3, 4 3, 3, 3
5
10+
1, 4, 5 2, 3, 5 2, 4, 4 3, 3, 4
4
11+
1, 5, 5 2, 4, 5 3, 3, 5 3, 4, 4
4
12+
2, 5, 5 3, 4, 5 4, 4, 4
3
13+
3, 5, 5 4, 4, 5
2
14+
4, 5, 5
1
15+
5, 5, 5
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, 2, 5 1, 1, 3, 4 1, 2, 2, 4 1, 2, 3, 3 2, 2, 2, 3
5
10+
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
7
11+
1, 1, 4, 5 1, 2, 3, 5 1, 2, 4, 4 1, 3, 3, 4 2, 2, 2, 5 2, 2, 3, 4 2, 3, 3, 3
7
12+
1, 1, 5, 5 1, 2, 4, 5 1, 3, 3, 5 1, 3, 4, 4 2, 2, 3, 5 2, 2, 4, 4 2, 3, 3, 4 3, 3, 3, 3
8
13+
1, 2, 5, 5 1, 3, 4, 5 1, 4, 4, 4 2, 2, 4, 5 2, 3, 3, 5 2, 3, 4, 4 3, 3, 3, 4
7
14+
1, 3, 5, 5 1, 4, 4, 5 2, 2, 5, 5 2, 3, 4, 5 2, 4, 4, 4 3, 3, 3, 5 3, 3, 4, 4
7
15+
1, 4, 5, 5 2, 3, 5, 5 2, 4, 4, 5 3, 3, 4, 5 3, 4, 4, 4
5
16+
1, 5, 5, 5 2, 4, 5, 5 3, 3, 5, 5 3, 4, 4, 5 4, 4, 4, 4
5
17+
2, 5, 5, 5 3, 4, 5, 5 4, 4, 4, 5
3
18+
3, 5, 5, 5 4, 4, 5, 5
2
19+
4, 5, 5, 5
1
20+
5, 5, 5, 5
1

− Subtraction

2-Cell Cages

Target Possible Combinations Count
1−
1, 2 2, 3 3, 4 4, 5
4
2−
1, 3 2, 4 3, 5
3
3−
1, 4 2, 5
2
4−
1, 5
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×
2, 3
1
8×
2, 4
1
9×
3, 3
1
10×
2, 5
1
12×
3, 4
1
15×
3, 5
1
16×
4, 4
1
20×
4, 5
1
25×
5, 5
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, 2, 3
1
8×
1, 2, 4 2, 2, 2
2
9×
1, 3, 3
1
10×
1, 2, 5
1
12×
1, 3, 4 2, 2, 3
2
15×
1, 3, 5
1
16×
1, 4, 4 2, 2, 4
2
18×
2, 3, 3
1
20×
1, 4, 5 2, 2, 5
2
24×
2, 3, 4
1
25×
1, 5, 5
1
27×
3, 3, 3
1
30×
2, 3, 5
1
32×
2, 4, 4
1
36×
3, 3, 4
1
40×
2, 4, 5
1
45×
3, 3, 5
1
48×
3, 4, 4
1
50×
2, 5, 5
1
60×
3, 4, 5
1
64×
4, 4, 4
1
75×
3, 5, 5
1
80×
4, 4, 5
1
100×
4, 5, 5
1
125×
5, 5, 5
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, 2, 3
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, 3, 4 1, 2, 2, 3
2
15×
1, 1, 3, 5
1
16×
1, 1, 4, 4 1, 2, 2, 4 2, 2, 2, 2
3
18×
1, 2, 3, 3
1
20×
1, 1, 4, 5 1, 2, 2, 5
2
24×
1, 2, 3, 4 2, 2, 2, 3
2
25×
1, 1, 5, 5
1
27×
1, 3, 3, 3
1
30×
1, 2, 3, 5
1
32×
1, 2, 4, 4 2, 2, 2, 4
2
36×
1, 3, 3, 4 2, 2, 3, 3
2
40×
1, 2, 4, 5 2, 2, 2, 5
2
45×
1, 3, 3, 5
1
48×
1, 3, 4, 4 2, 2, 3, 4
2
50×
1, 2, 5, 5
1
54×
2, 3, 3, 3
1
60×
1, 3, 4, 5 2, 2, 3, 5
2
64×
1, 4, 4, 4 2, 2, 4, 4
2
72×
2, 3, 3, 4
1
75×
1, 3, 5, 5
1
80×
1, 4, 4, 5 2, 2, 4, 5
2
81×
3, 3, 3, 3
1
90×
2, 3, 3, 5
1
96×
2, 3, 4, 4
1
100×
1, 4, 5, 5 2, 2, 5, 5
2
108×
3, 3, 3, 4
1
120×
2, 3, 4, 5
1
125×
1, 5, 5, 5
1
128×
2, 4, 4, 4
1
135×
3, 3, 3, 5
1
144×
3, 3, 4, 4
1
150×
2, 3, 5, 5
1
160×
2, 4, 4, 5
1
180×
3, 3, 4, 5
1
192×
3, 4, 4, 4
1
200×
2, 4, 5, 5
1
225×
3, 3, 5, 5
1
240×
3, 4, 4, 5
1
250×
2, 5, 5, 5
1
256×
4, 4, 4, 4
1
300×
3, 4, 5, 5
1
320×
4, 4, 4, 5
1
375×
3, 5, 5, 5
1
400×
4, 4, 5, 5
1
500×
4, 5, 5, 5
1
625×
5, 5, 5, 5
1

÷ Division

2-Cell Cages

Target Possible Combinations Count
2÷
1, 2 2, 4
2
3÷
1, 3
1
4÷
1, 4
1
5÷
1, 5
1
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