UNIQUE BLOCKS are essential tools for solving Kakuro and Killer Sudoku/Addoku puzzles. For example a total of 4 in 2 squares is a UNIQUE BLOCK. It can’t be 2 + 2 because each line of numbers can contain only one of each numeral. So the two squares can have only 1 or 3, though you don’t know in what order the 1 and 3 go until you look at the other sums around them.

This table gives you all the Unique blocks between 2 and 8 cells in length.

TOTAL
SQUARES
POSSIBLE NUMBERS
CAN’T HAVE
3
2
1,2
3,4,5,6,7,8,9
4
2
1,3
2,4,5,6,7,8,9
16
2
7,9
1,2,3,4,5,6,8
17
2
8,9
1,2,3,4,5,6,7
 
6
3
1,2,3
4,5,6,7,8,9
7
3
1,2,4
3,5,6,7,8,9
23
3
6,8,9
1,2,3,4,5,7
24
3
7,8,9
1,2,3,4,5,6
 
10
4
1,2,3,4
5,6,7,8,9
11
4
1,2,3,5
4,6,7,8,9
29
4
5,7,8,9
1,2,3,4,6
30
4
6,7,8,9
1,2,3,4,5
 
15
5
1,2,3,4,5
6,7,8,9
16
5
1,2,3,4,6
5,7,8,9
34
5
4,6,7,8,9
1,2,3,5
35
5
5,6,7,8,9
1,2,3,4
 
21
6
1,2,3,4,5,6
7,8,9
22
6
1,2,3,4,5,7
6,8,9
38
6
3,5,6,7,8,9
1,2,4
39
6
4,5,6,7,8,9
1,2,3
 
28
7
1,2,3,4,5,6,7
8,9
29
7
1,2,3,4,5,6,8
7,9
41
7
2,4,5,6,7,8,9
1,3
42
7
3,4,5,6,7,8,9
1,2
 
36
8
1,2,3,4,5,6,7,8
9
37
8
1,2,3,4,5,6,7,9
8
38
8
1,2,3,4,5,6,8,9
7
39
8
1,2,3,4,5,7,8,9
6
40
8
1,2,3,4,6,7,8,9
5
41
8
1,2,3,5,6,7,8,9
4
42
8
1,2,4,5,6,7,8,9
3
43
8
1,3,4,5,6,7,8,9
2
44
8
2,3,4,5,6,7,8,9
1

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