KenKen Puzzles

4×4 Cage Combinations

All valid digit combinations for 4×4 KenKen cages using digits 1–4.

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

− Subtraction

2-Cell Cages

Target Possible Combinations Count
1−
1, 2 2, 3 3, 4
3
2−
1, 3 2, 4
2
3−
1, 4
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
6×
2, 3
1
8×
2, 4
1
9×
3, 3
1
12×
3, 4
1
16×
4, 4
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
6×
1, 2, 3
1
8×
1, 2, 4 2, 2, 2
2
9×
1, 3, 3
1
12×
1, 3, 4 2, 2, 3
2
16×
1, 4, 4 2, 2, 4
2
18×
2, 3, 3
1
24×
2, 3, 4
1
27×
3, 3, 3
1
32×
2, 4, 4
1
36×
3, 3, 4
1
48×
3, 4, 4
1
64×
4, 4, 4
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
6×
1, 1, 2, 3
1
8×
1, 1, 2, 4 1, 2, 2, 2
2
9×
1, 1, 3, 3
1
12×
1, 1, 3, 4 1, 2, 2, 3
2
16×
1, 1, 4, 4 1, 2, 2, 4 2, 2, 2, 2
3
18×
1, 2, 3, 3
1
24×
1, 2, 3, 4 2, 2, 2, 3
2
27×
1, 3, 3, 3
1
32×
1, 2, 4, 4 2, 2, 2, 4
2
36×
1, 3, 3, 4 2, 2, 3, 3
2
48×
1, 3, 4, 4 2, 2, 3, 4
2
54×
2, 3, 3, 3
1
64×
1, 4, 4, 4 2, 2, 4, 4
2
72×
2, 3, 3, 4
1
81×
3, 3, 3, 3
1
96×
2, 3, 4, 4
1
108×
3, 3, 3, 4
1
128×
2, 4, 4, 4
1
144×
3, 3, 4, 4
1
192×
3, 4, 4, 4
1
256×
4, 4, 4, 4
1

÷ Division

2-Cell Cages

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