# Chinese Wooden Puzzles in N by 4

Below the results for the Chinese Wooden Puzzle that fit in a frame of size
N by 4 for all possible values for N and combination of
kind of pieces, where 2 pieces of each selected kind are used.
This page is generated with the program genCWP10.cpp
## Chinese Wooden Puzzles in 1 by 4

The one solution is symmetric in two directions.
The one pattern is:

## Chinese Wooden Puzzles in 2 by 4

The one normalized solution is symmetric in one direction.
The one pattern is:

The one solution is symmetric in two directions.
The one pattern is:

The one solution is symmetric in two directions.
The one pattern is:

## Chinese Wooden Puzzles in 3 by 4

The one normalized solution is not symmetric in any direction.
The one pattern is:

Five normalized solutions are not symmetric in any direction.
Four solutions (one normalized solution) are permutations of two solutions of blue, one solution of purple.
This leaves 16 mix solutions.
One pattern is a combination of two smaller patterns.
Three patterns are a mix patterns.
There is one optimal minimal touching pattern.
There are two maximal touching patterns.
The patterns are:

The one normalized solution is symmetric in one direction.
Two solutions (one normalized solution) are permutations of one solution of green, one solution of purple.
There are no mix solutions.
All patterns are a combination of two smaller patterns.
The one pattern is:

The one normalized solution is symmetric in one direction.
Two solutions (one normalized solution) are permutations of one solution of black, one solution of purple.
There are no mix solutions.
All patterns are a combination of two smaller patterns.
The one pattern is:

## Chinese Wooden Puzzles in 4 by 4

Two normalized solutions are not symmetric in any direction.
Four solutions (one normalized solution) are permutations of one solution of green, two solutions of blue.
This leaves four mix solutions.
One pattern is a combination of two smaller patterns.
One pattern is a mix patterns.
The patterns are:

Two normalized solutions are not symmetric in any direction.
Four solutions (one normalized solution) are permutations of one solution of black, two solutions of blue.
This leaves four mix solutions.
One pattern is a combination of two smaller patterns.
One pattern is a mix patterns.
The patterns are:

Two normalized solutions are symmetric in one direction.
Two solutions (one normalized solution) are permutations of one solution of black, one solution of green.
This leaves two mix solutions.
One pattern is a combination of two smaller patterns.
One pattern is a mix patterns.
The patterns are:

## Chinese Wooden Puzzles in 5 by 4

Two normalized solutions are not symmetric in any direction.
There is one minimal touching pattern, which is suboptimal with two extra.
There is one maximal touching pattern.
The patterns are:

Nine normalized solutions are not symmetric in any direction.
16 solutions (four normalized solutions) are permutations of four solutions of yellow and purple, two solutions of blue.
This leaves 20 mix solutions.
Two patterns are a combination of two smaller patterns.
Four patterns are a mix patterns.
There is one minimal touching pattern, which is suboptimal with two extra.
There are two maximal touching patterns.
The patterns are:

Two normalized solutions are not symmetric in any direction.
Eight solutions (two normalized solutions) are permutations of four solutions of yellow and purple, one solution of green.
There are no mix solutions.
All patterns are a combination of two smaller patterns.
The patterns are:

18 normalized solutions are not symmetric in any direction.
32 solutions (eight normalized solutions) are permutations of 16 solutions of blue and purple, one solution of green.
Eight solutions (two normalized solutions) are permutations of four solutions of blue and green, one solution of purple.
There are a total of 40 solutions (ten normalized solutions) that are permutations, leaving 32 mix solutions.
Seven patterns are a combination of two smaller patterns.
Three patterns are a combination of three smaller patterns.
Three patterns are a mix patterns.
There are four minimal touching patterns, which are suboptimal with one extra.
There are seven maximal touching patterns.
The patterns are:

Six normalized solutions are not symmetric in any direction.
Eight solutions (two normalized solutions) are permutations of four solutions of yellow and purple, one solution of black.
This leaves 16 mix solutions.
Two patterns are a combination of two smaller patterns.
Four patterns are a mix patterns.
There are four minimal touching patterns, which are suboptimal with two extra.
There are two maximal touching patterns.
The patterns are:

38 normalized solutions are not symmetric in any direction.
32 solutions (eight normalized solutions) are permutations of 16 solutions of blue and purple, one solution of black.
Eight solutions (two normalized solutions) are permutations of four solutions of blue and black, one solution of purple.
There are a total of 40 solutions (ten normalized solutions) that are permutations, leaving 112 mix solutions.
Seven patterns are a combination of two smaller patterns.
Three patterns are a combination of three smaller patterns.
15 patterns are a mix patterns.
There are four optimal minimal touching patterns.
There are seven maximal touching patterns.
The patterns are:

Three normalized solutions are symmetric in one direction.
Four normalized solutions are not symmetric in any direction.
Four solutions (one normalized solution) are permutations of two solutions of green and black, one solution of purple.
This leaves 18 mix solutions.
One pattern is a combination of two smaller patterns.
Three patterns are a combination of three smaller patterns.
Three patterns are a mix patterns.
There are three minimal touching patterns, which are suboptimal with one extra.
There are four maximal touching patterns.
The patterns are:

The one normalized solution is not symmetric in any direction.
The one pattern is:

## Chinese Wooden Puzzles in 6 by 4

Ten normalized solutions are not symmetric in any direction.
Eight solutions (two normalized solutions) are permutations of four solutions of blue and green, one solution of black.
Eight solutions (two normalized solutions) are permutations of four solutions of blue and black, one solution of green.
Eight solutions (two normalized solutions) are permutations of two solutions of green and black, two solutions of blue.
There are a total of 24 solutions (six normalized solutions) that are permutations, leaving 16 mix solutions.
Three patterns are a combination of two smaller patterns.
Three patterns are a combination of three smaller patterns.
One pattern is a mix patterns.
There is one minimal touching pattern, which is suboptimal with one extra.
There are six maximal touching patterns.
The patterns are:

The one normalized solution is symmetric in one direction.
The one pattern is:

## Chinese Wooden Puzzles in 7 by 4

25 normalized solutions are not symmetric in any direction.
32 solutions (eight normalized solutions) are permutations of eight solutions of red, yellow, and purple, two solutions of blue.
This leaves 68 mix solutions.
Four patterns are a combination of two smaller patterns.
17 patterns are a mix patterns.
There are three minimal touching patterns, which are suboptimal with two extra.
There are three maximal touching patterns.
The patterns are:

Four normalized solutions are not symmetric in any direction.
16 solutions (four normalized solutions) are permutations of eight solutions of red, yellow, and purple, one solution of green.
There are no mix solutions.
All patterns are a combination of two smaller patterns.
There are two minimal touching patterns, which are suboptimal with three extra.
There are two maximal touching patterns.
The patterns are:

36 normalized solutions are not symmetric in any direction.
32 solutions (eight normalized solutions) are permutations of four solutions of blue and green, four solutions of yellow and purple.
40 solutions (ten normalized solutions) are permutations of 20 solutions of yellow, blue, and purple, one solution of green.
There are a total of 72 solutions (18 normalized solutions) that are permutations, leaving 72 mix solutions.
12 patterns are a combination of two smaller patterns.
Six patterns are a combination of three smaller patterns.
Five patterns are a mix patterns.
There are four minimal touching patterns, which are suboptimal with three extra.
There are ten maximal touching patterns.
The patterns are:

Eight normalized solutions are not symmetric in any direction.
16 solutions (four normalized solutions) are permutations of eight solutions of red, yellow, and purple, one solution of black.
This leaves 16 mix solutions.
Four patterns are a combination of two smaller patterns.
Four patterns are a mix patterns.
There is one minimal touching pattern, which is suboptimal with two extra.
There are five maximal touching patterns.
The patterns are:

Two normalized solutions are not symmetric in any direction.
The one pattern is:

62 normalized solutions are not symmetric in any direction.
32 solutions (eight normalized solutions) are permutations of four solutions of blue and black, four solutions of yellow and purple.
40 solutions (ten normalized solutions) are permutations of 20 solutions of yellow, blue, and purple, one solution of black.
64 solutions (16 normalized solutions) are permutations of 16 solutions of yellow, black, and purple, two solutions of blue.
There are a total of 136 solutions (34 normalized solutions) that are permutations, leaving 112 mix solutions.
20 patterns are a combination of two smaller patterns.
Six patterns are a combination of three smaller patterns.
14 patterns are a mix patterns.
There are two minimal touching patterns, which are suboptimal with two extra.
There are ten maximal touching patterns.
The patterns are:

18 normalized solutions are not symmetric in any direction.
16 solutions (four normalized solutions) are permutations of two solutions of green and black, four solutions of yellow and purple.
32 solutions (eight normalized solutions) are permutations of 16 solutions of yellow, black, and purple, one solution of green.
There are a total of 48 solutions (12 normalized solutions) that are permutations, leaving 24 mix solutions.
All patterns are a combination of smaller patterns.
12 patterns are a combination of two smaller patterns.
Six patterns are a combination of three smaller patterns.
There are eight minimal touching patterns, which are suboptimal with three extra.
There are ten maximal touching patterns.
The patterns are:

156 normalized solutions are not symmetric in any direction.
24 solutions (six normalized solutions) are permutations of four solutions of blue and green, one solution of black, one solution of purple.
24 solutions (six normalized solutions) are permutations of four solutions of blue and black, one solution of green, one solution of purple.
24 solutions (six normalized solutions) are permutations of two solutions of green and black, two solutions of blue, one solution of purple.
64 solutions (16 normalized solutions) are permutations of two solutions of green and black, 16 solutions of blue and purple.
64 solutions (16 normalized solutions) are permutations of 32 solutions of blue, green, and purple, one solution of black.
224 solutions (56 normalized solutions) are permutations of 112 solutions of blue, black, and purple, one solution of green.
72 solutions (18 normalized solutions) are permutations of 18 solutions of green, black, and purple, two solutions of blue.
32 solutions (eight normalized solutions) are permutations of 16 solutions of blue, green, and black, one solution of purple.
There are a total of 528 solutions (132 normalized solutions) that are permutations, leaving 96 mix solutions.
54 patterns are a combination of two smaller patterns.
27 patterns are a combination of three smaller patterns.
12 patterns are a combination of four smaller patterns.
Six patterns are a mix patterns.
There are ten minimal touching patterns, which are suboptimal with one extra.
There are 37 maximal touching patterns.
The patterns are:

Three normalized solutions are not symmetric in any direction.
There is one minimal touching pattern, which is suboptimal with four extra.
There is one maximal touching pattern.
The patterns are:

Three normalized solutions are not symmetric in any direction.
There is one minimal touching pattern, which is suboptimal with five extra.
There are two maximal touching patterns.
The patterns are:

14 normalized solutions are not symmetric in any direction.
16 solutions (four normalized solutions) are permutations of four solutions of orange, white, and purple, two solutions of blue.
Four solutions (one normalized solution) are permutations of two solutions of orange, blue, and white, one solution of purple.
There are a total of 20 solutions (five normalized solutions) that are permutations, leaving 36 mix solutions.
Three patterns are a combination of two smaller patterns.
Seven patterns are a mix patterns.
There are three minimal touching patterns, which are suboptimal with one extra.
There are two maximal touching patterns.
The patterns are:

Two normalized solutions are not symmetric in any direction.
Eight solutions (two normalized solutions) are permutations of four solutions of orange, white, and purple, one solution of green.
There are no mix solutions.
All patterns are a combination of two smaller patterns.
The patterns are:

Three normalized solutions are not symmetric in any direction.
Eight solutions (two normalized solutions) are permutations of four solutions of orange, white, and purple, one solution of black.
This leaves four mix solutions.
Two patterns are a combination of two smaller patterns.
One pattern is a mix patterns.
There is one minimal touching pattern, which is suboptimal with four extra.
There are two maximal touching patterns.
The patterns are:

## Chinese Wooden Puzzles in 8 by 4

Five normalized solutions are not symmetric in any direction.
There are two minimal touching patterns, which are suboptimal with four extra.
There is one maximal touching pattern.
The patterns are:

Two normalized solutions are not symmetric in any direction.
There is one minimal touching pattern, which is suboptimal with six extra.
There is one maximal touching pattern.
The patterns are:

The one normalized solution is not symmetric in any direction.
Four solutions (one normalized solution) are permutations of two solutions of orange, blue, and white, one solution of green.
There are no mix solutions.
All patterns are a combination of two smaller patterns.
The one pattern is:

Two normalized solutions are not symmetric in any direction.
The one pattern is:

Four normalized solutions are not symmetric in any direction.
The patterns are:

Seven normalized solutions are not symmetric in any direction.
Four solutions (one normalized solution) are permutations of two solutions of orange, blue, and white, one solution of black.
This leaves 24 mix solutions.
One pattern is a combination of two smaller patterns.
Four patterns are a mix patterns.
There are two minimal touching patterns, which are suboptimal with one extra.
There is one maximal touching pattern.
The patterns are:

## Chinese Wooden Puzzles in 9 by 4

80 normalized solutions are not symmetric in any direction.
96 solutions (24 normalized solutions) are permutations of eight solutions of red, yellow, and purple, one solution of green, two solutions of blue.
64 solutions (16 normalized solutions) are permutations of eight solutions of red, yellow, and purple, four solutions of blue and green.
136 solutions (34 normalized solutions) are permutations of 68 solutions of red, yellow, blue, and purple, one solution of green.
There are a total of 296 solutions (74 normalized solutions) that are permutations, leaving 24 mix solutions.
42 patterns are a combination of two smaller patterns.
12 patterns are a combination of three smaller patterns.
Six patterns are a mix patterns.
There are six minimal touching patterns, which are suboptimal with three extra.
There are 12 maximal touching patterns.
The patterns are:

150 normalized solutions are not symmetric in any direction.
96 solutions (24 normalized solutions) are permutations of eight solutions of red, yellow, and purple, one solution of black, two solutions of blue.
64 solutions (16 normalized solutions) are permutations of eight solutions of red, yellow, and purple, four solutions of blue and black.
136 solutions (34 normalized solutions) are permutations of 68 solutions of red, yellow, blue, and purple, one solution of black.
64 solutions (16 normalized solutions) are permutations of 16 solutions of red, yellow, black, and purple, two solutions of blue.
There are a total of 360 solutions (90 normalized solutions) that are permutations, leaving 240 mix solutions.
50 patterns are a combination of two smaller patterns.
12 patterns are a combination of three smaller patterns.
59 patterns are a mix patterns.
There is one optimal minimal touching pattern.
There are 18 maximal touching patterns.
The patterns are:

29 normalized solutions are not symmetric in any direction.
48 solutions (12 normalized solutions) are permutations of eight solutions of red, yellow, and purple, one solution of black, one solution of green.
32 solutions (eight normalized solutions) are permutations of eight solutions of red, yellow, and purple, two solutions of green and black.
32 solutions (eight normalized solutions) are permutations of 16 solutions of red, yellow, black, and purple, one solution of green.
There are a total of 112 solutions (28 normalized solutions) that are permutations, leaving four mix solutions.
16 patterns are a combination of two smaller patterns.
12 patterns are a combination of three smaller patterns.
One pattern is a mix patterns.
There are two minimal touching patterns, which are suboptimal with three extra.
There are 16 maximal touching patterns.
The patterns are:

Six normalized solutions are not symmetric in any direction.
16 solutions (four normalized solutions) are permutations of eight solutions of red, blue, black, and purple, one solution of green.
This leaves eight mix solutions.
Two patterns are a combination of two smaller patterns.
One pattern is a mix patterns.
The patterns are:

325 normalized solutions are not symmetric in any direction.
120 solutions (30 normalized solutions) are permutations of 20 solutions of yellow, blue, and purple, one solution of black, one solution of green.
80 solutions (20 normalized solutions) are permutations of 20 solutions of yellow, blue, and purple, two solutions of green and black.
192 solutions (48 normalized solutions) are permutations of 16 solutions of yellow, black, and purple, one solution of green, two solutions of blue.
128 solutions (32 normalized solutions) are permutations of 16 solutions of yellow, black, and purple, four solutions of blue and green.
128 solutions (32 normalized solutions) are permutations of 16 solutions of blue, green, and black, four solutions of yellow and purple.
144 solutions (36 normalized solutions) are permutations of 72 solutions of yellow, blue, green, and purple, one solution of black.
224 solutions (56 normalized solutions) are permutations of 112 solutions of yellow, blue, black, and purple, one solution of green.
96 solutions (24 normalized solutions) are permutations of 24 solutions of yellow, green, black, and purple, two solutions of blue.
There are a total of 1,112 solutions (278 normalized solutions) that are permutations, leaving 188 mix solutions.
78 patterns are a combination of two smaller patterns.
84 patterns are a combination of three smaller patterns.
24 patterns are a combination of four smaller patterns.
20 patterns are a mix patterns.
There are 22 minimal touching patterns, which are suboptimal with three extra.
There are 60 maximal touching patterns.
The patterns are:

13 normalized solutions are not symmetric in any direction.
There are two minimal touching patterns, which are suboptimal with four extra.
There are four maximal touching patterns.
The patterns are:

97 normalized solutions are not symmetric in any direction.
48 solutions (12 normalized solutions) are permutations of 12 solutions of orange, red, white, and purple, two solutions of blue.
40 solutions (ten normalized solutions) are permutations of 20 solutions of orange, red, blue, and white, one solution of purple.
There are a total of 88 solutions (22 normalized solutions) that are permutations, leaving 300 mix solutions.
Ten patterns are a combination of two smaller patterns.
51 patterns are a mix patterns.
There is one minimal touching pattern, which is suboptimal with one extra.
There are three maximal touching patterns.
The patterns are:

100 normalized solutions are not symmetric in any direction.
16 solutions (four normalized solutions) are permutations of two solutions of orange, blue, and white, four solutions of yellow and purple.
48 solutions (12 normalized solutions) are permutations of 12 solutions of orange, yellow, white, and purple, two solutions of blue.
16 solutions (four normalized solutions) are permutations of eight solutions of orange, yellow, blue, and white, one solution of purple.
There are a total of 80 solutions (20 normalized solutions) that are permutations, leaving 320 mix solutions.
14 patterns are a combination of two smaller patterns.
61 patterns are a mix patterns.
There is one minimal touching pattern, which is suboptimal with one extra.
There is one maximal touching pattern.
The patterns are:

Ten normalized solutions are not symmetric in any direction.
24 solutions (six normalized solutions) are permutations of 12 solutions of orange, red, white, and purple, one solution of green.
This leaves 16 mix solutions.
Four patterns are a combination of two smaller patterns.
Two patterns are a mix patterns.
There are three minimal touching patterns, which are suboptimal with five extra.
There are three maximal touching patterns.
The patterns are:

12 normalized solutions are not symmetric in any direction.
24 solutions (six normalized solutions) are permutations of 12 solutions of orange, yellow, white, and purple, one solution of green.
This leaves 24 mix solutions.
Six patterns are a combination of two smaller patterns.
Three patterns are a mix patterns.
There is one minimal touching pattern, which is suboptimal with four extra.
There is one maximal touching pattern.
The patterns are:

59 normalized solutions are not symmetric in any direction.
48 solutions (12 normalized solutions) are permutations of four solutions of orange, white, and purple, one solution of green, two solutions of blue.
32 solutions (eight normalized solutions) are permutations of four solutions of orange, white, and purple, four solutions of blue and green.
12 solutions (three normalized solutions) are permutations of two solutions of orange, blue, and white, one solution of green, one solution of purple.
72 solutions (18 normalized solutions) are permutations of 36 solutions of orange, blue, white, and purple, one solution of green.
There are a total of 164 solutions (41 normalized solutions) that are permutations, leaving 72 mix solutions.
18 patterns are a combination of two smaller patterns.
Nine patterns are a combination of three smaller patterns.
Ten patterns are a mix patterns.
There are seven minimal touching patterns, which are suboptimal with two extra.
There are 12 maximal touching patterns.
The patterns are:

17 normalized solutions are not symmetric in any direction.
24 solutions (six normalized solutions) are permutations of 12 solutions of orange, red, white, and purple, one solution of black.
16 solutions (four normalized solutions) are permutations of eight solutions of orange, red, black, and white, one solution of purple.
There are a total of 40 solutions (ten normalized solutions) that are permutations, leaving 28 mix solutions.
Six patterns are a combination of two smaller patterns.
Five patterns are a mix patterns.
There are two minimal touching patterns, which are suboptimal with four extra.
There are five maximal touching patterns.
The patterns are:

63 normalized solutions are not symmetric in any direction.
24 solutions (six normalized solutions) are permutations of 12 solutions of orange, yellow, white, and purple, one solution of black.
32 solutions (eight normalized solutions) are permutations of 16 solutions of orange, yellow, black, and white, one solution of purple.
There are a total of 56 solutions (14 normalized solutions) that are permutations, leaving 196 mix solutions.
Ten patterns are a combination of two smaller patterns.
33 patterns are a mix patterns.
There are two minimal touching patterns, which are suboptimal with one extra.
There is one maximal touching pattern.
The patterns are:

112 normalized solutions are not symmetric in any direction.
48 solutions (12 normalized solutions) are permutations of four solutions of orange, white, and purple, one solution of black, two solutions of blue.
32 solutions (eight normalized solutions) are permutations of four solutions of orange, white, and purple, four solutions of blue and black.
12 solutions (three normalized solutions) are permutations of two solutions of orange, blue, and white, one solution of black, one solution of purple.
72 solutions (18 normalized solutions) are permutations of 36 solutions of orange, blue, white, and purple, one solution of black.
16 solutions (four normalized solutions) are permutations of four solutions of orange, black, white, and purple, two solutions of blue.
48 solutions (12 normalized solutions) are permutations of 24 solutions of orange, blue, black, and white, one solution of purple.
There are a total of 228 solutions (57 normalized solutions) that are permutations, leaving 220 mix solutions.
28 patterns are a combination of two smaller patterns.
Nine patterns are a combination of three smaller patterns.
35 patterns are a mix patterns.
There are seven minimal touching patterns, which are suboptimal with one extra.
There are 12 maximal touching patterns.
The patterns are:

15 normalized solutions are not symmetric in any direction.
24 solutions (six normalized solutions) are permutations of four solutions of orange, white, and purple, one solution of black, one solution of green.
16 solutions (four normalized solutions) are permutations of four solutions of orange, white, and purple, two solutions of green and black.
Eight solutions (two normalized solutions) are permutations of four solutions of orange, black, white, and purple, one solution of green.
There are a total of 48 solutions (12 normalized solutions) that are permutations, leaving 12 mix solutions.
Six patterns are a combination of two smaller patterns.
Six patterns are a combination of three smaller patterns.
Two patterns are a mix patterns.
There are two minimal touching patterns, which are suboptimal with five extra.
There are ten maximal touching patterns.
The patterns are:

## Chinese Wooden Puzzles in 10 by 4

Eight normalized solutions are not symmetric in any direction.
There is one minimal touching pattern, which is suboptimal with four extra.
There are two maximal touching patterns.
The patterns are:

Ten normalized solutions are not symmetric in any direction.
40 solutions (ten normalized solutions) are permutations of 20 solutions of orange, red, blue, and white, one solution of green.
There are no mix solutions.
All patterns are a combination of two smaller patterns.
There are four minimal touching patterns, which are suboptimal with five extra.
There are two maximal touching patterns.
The patterns are:

Four normalized solutions are not symmetric in any direction.
16 solutions (four normalized solutions) are permutations of eight solutions of orange, yellow, blue, and white, one solution of green.
There are no mix solutions.
All patterns are a combination of two smaller patterns.
There are two minimal touching patterns, which are suboptimal with seven extra.
There are two maximal touching patterns.
The patterns are:

25 normalized solutions are not symmetric in any direction.
40 solutions (ten normalized solutions) are permutations of 20 solutions of orange, red, blue, and white, one solution of black.
32 solutions (eight normalized solutions) are permutations of eight solutions of orange, red, black, and white, two solutions of blue.
There are a total of 72 solutions (18 normalized solutions) that are permutations, leaving 28 mix solutions.
Eight patterns are a combination of two smaller patterns.
Five patterns are a mix patterns.
There is one minimal touching pattern, which is suboptimal with one extra.
There are two maximal touching patterns.
The patterns are:

56 normalized solutions are not symmetric in any direction.
16 solutions (four normalized solutions) are permutations of eight solutions of orange, yellow, blue, and white, one solution of black.
64 solutions (16 normalized solutions) are permutations of 16 solutions of orange, yellow, black, and white, two solutions of blue.
There are a total of 80 solutions (20 normalized solutions) that are permutations, leaving 144 mix solutions.
Eight patterns are a combination of two smaller patterns.
26 patterns are a mix patterns.
There is one minimal touching pattern, which is suboptimal with one extra.
There are two maximal touching patterns.
The patterns are:

Four normalized solutions are not symmetric in any direction.
16 solutions (four normalized solutions) are permutations of eight solutions of orange, red, black, and white, one solution of green.
There are no mix solutions.
All patterns are a combination of two smaller patterns.
The patterns are:

Ten normalized solutions are not symmetric in any direction.
32 solutions (eight normalized solutions) are permutations of 16 solutions of orange, yellow, black, and white, one solution of green.
This leaves eight mix solutions.
Four patterns are a combination of two smaller patterns.
One pattern is a mix patterns.
The patterns are:

17 normalized solutions are not symmetric in any direction.
12 solutions (three normalized solutions) are permutations of two solutions of orange, blue, and white, one solution of black, one solution of green.
Eight solutions (two normalized solutions) are permutations of two solutions of orange, blue, and white, two solutions of green and black.
48 solutions (12 normalized solutions) are permutations of 24 solutions of orange, blue, black, and white, one solution of green.
There are a total of 68 solutions (17 normalized solutions) that are permutations, leaving no mix solutions.
All patterns are a combination of smaller patterns.
Ten patterns are a combination of two smaller patterns.
Three patterns are a combination of three smaller patterns.
There are four minimal touching patterns, which are suboptimal with two extra.
There are two maximal touching patterns.
The patterns are:

## Chinese Wooden Puzzles in 11 by 4

671 normalized solutions are not symmetric in any direction.
256 solutions (64 normalized solutions) are permutations of 16 solutions of blue, green, and black, eight solutions of red, yellow, and purple.
408 solutions (102 normalized solutions) are permutations of 68 solutions of red, yellow, blue, and purple, one solution of black, one solution of green.
272 solutions (68 normalized solutions) are permutations of 68 solutions of red, yellow, blue, and purple, two solutions of green and black.
192 solutions (48 normalized solutions) are permutations of 16 solutions of red, yellow, black, and purple, one solution of green, two solutions of blue.
128 solutions (32 normalized solutions) are permutations of 16 solutions of red, yellow, black, and purple, four solutions of blue and green.
48 solutions (12 normalized solutions) are permutations of 24 solutions of red, yellow, blue, green, and purple, one solution of black.
480 solutions (120 normalized solutions) are permutations of 240 solutions of red, yellow, blue, black, and purple, one solution of green.
16 solutions (four normalized solutions) are permutations of four solutions of red, yellow, green, black, and purple, two solutions of blue.
There are a total of 1,800 solutions (450 normalized solutions) that are permutations, leaving 884 mix solutions.
232 patterns are a combination of two smaller patterns.
198 patterns are a combination of three smaller patterns.
48 patterns are a combination of four smaller patterns.
29 patterns are a mix patterns.
There are two minimal touching patterns, which are suboptimal with one extra.
There are 100 maximal touching patterns.
The patterns are:

424 normalized solutions are not symmetric in any direction.
32 solutions (eight normalized solutions) are permutations of two solutions of orange, blue, and white, eight solutions of red, yellow, and purple.
160 solutions (40 normalized solutions) are permutations of 20 solutions of orange, red, blue, and white, four solutions of yellow and purple.
208 solutions (52 normalized solutions) are permutations of 52 solutions of orange, red, yellow, white, and purple, two solutions of blue.
64 solutions (16 normalized solutions) are permutations of 32 solutions of orange, red, yellow, blue, and white, one solution of purple.
There are a total of 464 solutions (116 normalized solutions) that are permutations, leaving 1,232 mix solutions.
72 patterns are a combination of two smaller patterns.
259 patterns are a mix patterns.
There are two minimal touching patterns, which are suboptimal with one extra.
There is one maximal touching pattern.
The patterns are:

34 normalized solutions are not symmetric in any direction.
104 solutions (26 normalized solutions) are permutations of 52 solutions of orange, red, yellow, white, and purple, one solution of green.
This leaves 32 mix solutions.
24 patterns are a combination of two smaller patterns.
Five patterns are a mix patterns.
There is one minimal touching pattern, which is suboptimal with four extra.
There is one maximal touching pattern.
The patterns are:

327 normalized solutions are not symmetric in any direction.
144 solutions (36 normalized solutions) are permutations of 12 solutions of orange, red, white, and purple, one solution of green, two solutions of blue.
96 solutions (24 normalized solutions) are permutations of 12 solutions of orange, red, white, and purple, four solutions of blue and green.
120 solutions (30 normalized solutions) are permutations of 20 solutions of orange, red, blue, and white, one solution of green, one solution of purple.
600 solutions (150 normalized solutions) are permutations of 300 solutions of orange, red, blue, white, and purple, one solution of green.
64 solutions (16 normalized solutions) are permutations of 16 solutions of orange, red, green, white, and purple, two solutions of blue.
There are a total of 1,024 solutions (256 normalized solutions) that are permutations, leaving 284 mix solutions.
114 patterns are a combination of two smaller patterns.
30 patterns are a combination of three smaller patterns.
39 patterns are a mix patterns.
There are two minimal touching patterns, which are suboptimal with two extra.
There are 16 maximal touching patterns.
The patterns are:

350 normalized solutions are not symmetric in any direction.
48 solutions (12 normalized solutions) are permutations of two solutions of orange, blue, and white, four solutions of yellow and purple, one solution of green.
144 solutions (36 normalized solutions) are permutations of 12 solutions of orange, yellow, white, and purple, one solution of green, two solutions of blue.
96 solutions (24 normalized solutions) are permutations of 12 solutions of orange, yellow, white, and purple, four solutions of blue and green.
48 solutions (12 normalized solutions) are permutations of eight solutions of orange, yellow, blue, and white, one solution of green, one solution of purple.
640 solutions (160 normalized solutions) are permutations of 320 solutions of orange, yellow, blue, white, and purple, one solution of green.
96 solutions (24 normalized solutions) are permutations of 24 solutions of orange, yellow, green, white, and purple, two solutions of blue.
There are a total of 1,072 solutions (268 normalized solutions) that are permutations, leaving 328 mix solutions.
140 patterns are a combination of two smaller patterns.
42 patterns are a combination of three smaller patterns.
49 patterns are a mix patterns.
There are four minimal touching patterns, which are suboptimal with two extra.
There are four maximal touching patterns.
The patterns are:

139 normalized solutions are not symmetric in any direction.
64 solutions (16 normalized solutions) are permutations of eight solutions of orange, red, black, and white, four solutions of yellow and purple.
104 solutions (26 normalized solutions) are permutations of 52 solutions of orange, red, yellow, white, and purple, one solution of black.
There are a total of 168 solutions (42 normalized solutions) that are permutations, leaving 388 mix solutions.
32 patterns are a combination of two smaller patterns.
79 patterns are a mix patterns.
There are two minimal touching patterns, which are suboptimal with one extra.
There is one maximal touching pattern.
The patterns are:

738 normalized solutions are not symmetric in any direction.
144 solutions (36 normalized solutions) are permutations of 12 solutions of orange, red, white, and purple, one solution of black, two solutions of blue.
96 solutions (24 normalized solutions) are permutations of 12 solutions of orange, red, white, and purple, four solutions of blue and black.
120 solutions (30 normalized solutions) are permutations of 20 solutions of orange, red, blue, and white, one solution of black, one solution of purple.
96 solutions (24 normalized solutions) are permutations of eight solutions of orange, red, black, and white, two solutions of blue, one solution of purple.
256 solutions (64 normalized solutions) are permutations of eight solutions of orange, red, black, and white, 16 solutions of blue and purple.
600 solutions (150 normalized solutions) are permutations of 300 solutions of orange, red, blue, white, and purple, one solution of black.
112 solutions (28 normalized solutions) are permutations of 28 solutions of orange, red, black, white, and purple, two solutions of blue.
56 solutions (14 normalized solutions) are permutations of 28 solutions of orange, red, blue, black, and white, one solution of purple.
There are a total of 1,480 solutions (370 normalized solutions) that are permutations, leaving 1,472 mix solutions.
150 patterns are a combination of two smaller patterns.
36 patterns are a combination of three smaller patterns.
213 patterns are a mix patterns.
There are six minimal touching patterns, which are suboptimal with one extra.
There are 20 maximal touching patterns.
The patterns are:

1,650 normalized solutions are not symmetric in any direction.
48 solutions (12 normalized solutions) are permutations of two solutions of orange, blue, and white, four solutions of yellow and purple, one solution of black.
64 solutions (16 normalized solutions) are permutations of two solutions of orange, blue, and white, 16 solutions of yellow, black, and purple.
144 solutions (36 normalized solutions) are permutations of 12 solutions of orange, yellow, white, and purple, one solution of black, two solutions of blue.
96 solutions (24 normalized solutions) are permutations of 12 solutions of orange, yellow, white, and purple, four solutions of blue and black.
48 solutions (12 normalized solutions) are permutations of eight solutions of orange, yellow, blue, and white, one solution of black, one solution of purple.
192 solutions (48 normalized solutions) are permutations of 16 solutions of orange, yellow, black, and white, two solutions of blue, one solution of purple.
512 solutions (128 normalized solutions) are permutations of 16 solutions of orange, yellow, black, and white, 16 solutions of blue and purple.
192 solutions (48 normalized solutions) are permutations of 24 solutions of orange, blue, black, and white, four solutions of yellow and purple.
640 solutions (160 normalized solutions) are permutations of 320 solutions of orange, yellow, blue, white, and purple, one solution of black.
784 solutions (196 normalized solutions) are permutations of 196 solutions of orange, yellow, black, white, and purple, two solutions of blue.
288 solutions (72 normalized solutions) are permutations of 144 solutions of orange, yellow, blue, black, and white, one solution of purple.
There are a total of 3,008 solutions (752 normalized solutions) that are permutations, leaving 3,592 mix solutions.
340 patterns are a combination of two smaller patterns.
54 patterns are a combination of three smaller patterns.
602 patterns are a mix patterns.
There is one optimal minimal touching pattern.
There are four maximal touching patterns.
The patterns are:

81 normalized solutions are not symmetric in any direction.
72 solutions (18 normalized solutions) are permutations of 12 solutions of orange, red, white, and purple, one solution of black, one solution of green.
48 solutions (12 normalized solutions) are permutations of 12 solutions of orange, red, white, and purple, two solutions of green and black.
48 solutions (12 normalized solutions) are permutations of eight solutions of orange, red, black, and white, one solution of green, one solution of purple.
32 solutions (eight normalized solutions) are permutations of 16 solutions of orange, red, green, white, and purple, one solution of black.
56 solutions (14 normalized solutions) are permutations of 28 solutions of orange, red, black, white, and purple, one solution of green.
There are a total of 256 solutions (64 normalized solutions) that are permutations, leaving 68 mix solutions.
22 patterns are a combination of two smaller patterns.
18 patterns are a combination of three smaller patterns.
Nine patterns are a mix patterns.
There are ten minimal touching patterns, which are suboptimal with five extra.
There are 18 maximal touching patterns.
The patterns are:

206 normalized solutions are not symmetric in any direction.
72 solutions (18 normalized solutions) are permutations of 12 solutions of orange, yellow, white, and purple, one solution of black, one solution of green.
48 solutions (12 normalized solutions) are permutations of 12 solutions of orange, yellow, white, and purple, two solutions of green and black.
96 solutions (24 normalized solutions) are permutations of 16 solutions of orange, yellow, black, and white, one solution of green, one solution of purple.
48 solutions (12 normalized solutions) are permutations of 24 solutions of orange, yellow, green, white, and purple, one solution of black.
392 solutions (98 normalized solutions) are permutations of 196 solutions of orange, yellow, black, white, and purple, one solution of green.
16 solutions (four normalized solutions) are permutations of eight solutions of orange, yellow, green, black, and white, one solution of purple.
There are a total of 672 solutions (168 normalized solutions) that are permutations, leaving 152 mix solutions.
86 patterns are a combination of two smaller patterns.
30 patterns are a combination of three smaller patterns.
20 patterns are a mix patterns.
There are three minimal touching patterns, which are suboptimal with one extra.
There are four maximal touching patterns.
The patterns are:

552 normalized solutions are not symmetric in any direction.
128 solutions (32 normalized solutions) are permutations of 16 solutions of blue, green, and black, four solutions of orange, white, and purple.
24 solutions (six normalized solutions) are permutations of two solutions of orange, blue, and white, two solutions of green and black, one solution of purple.
72 solutions (18 normalized solutions) are permutations of two solutions of orange, blue, and white, 18 solutions of green, black, and purple.
216 solutions (54 normalized solutions) are permutations of 36 solutions of orange, blue, white, and purple, one solution of black, one solution of green.
144 solutions (36 normalized solutions) are permutations of 36 solutions of orange, blue, white, and purple, two solutions of green and black.
48 solutions (12 normalized solutions) are permutations of four solutions of orange, black, white, and purple, one solution of green, two solutions of blue.
32 solutions (eight normalized solutions) are permutations of four solutions of orange, black, white, and purple, four solutions of blue and green.
144 solutions (36 normalized solutions) are permutations of 24 solutions of orange, blue, black, and white, one solution of green, one solution of purple.
144 solutions (36 normalized solutions) are permutations of 72 solutions of orange, blue, green, white, and purple, one solution of black.
440 solutions (110 normalized solutions) are permutations of 220 solutions of orange, blue, black, white, and purple, one solution of green.
48 solutions (12 normalized solutions) are permutations of 12 solutions of orange, green, black, white, and purple, two solutions of blue.
There are a total of 1,440 solutions (360 normalized solutions) that are permutations, leaving 768 mix solutions.
146 patterns are a combination of two smaller patterns.
114 patterns are a combination of three smaller patterns.
36 patterns are a combination of four smaller patterns.
49 patterns are a mix patterns.
There are 34 minimal touching patterns, which are suboptimal with two extra.
There are 68 maximal touching patterns.
The patterns are:

## Chinese Wooden Puzzles in 12 by 4

18 normalized solutions are not symmetric in any direction.
64 solutions (16 normalized solutions) are permutations of 32 solutions of orange, red, yellow, blue, and white, one solution of green.
This leaves eight mix solutions.
16 patterns are a combination of two smaller patterns.
One pattern is a mix patterns.
There are two minimal touching patterns, which are suboptimal with five extra.
There are four maximal touching patterns.
The patterns are:

97 normalized solutions are not symmetric in any direction.
64 solutions (16 normalized solutions) are permutations of 32 solutions of orange, red, yellow, blue, and white, one solution of black.
This leaves 324 mix solutions.
16 patterns are a combination of two smaller patterns.
62 patterns are a mix patterns.
There are two minimal touching patterns, which are suboptimal with one extra.
There are nine maximal touching patterns.
The patterns are:

116 normalized solutions are not symmetric in any direction.
120 solutions (30 normalized solutions) are permutations of 20 solutions of orange, red, blue, and white, one solution of black, one solution of green.
80 solutions (20 normalized solutions) are permutations of 20 solutions of orange, red, blue, and white, two solutions of green and black.
96 solutions (24 normalized solutions) are permutations of eight solutions of orange, red, black, and white, one solution of green, two solutions of blue.
64 solutions (16 normalized solutions) are permutations of eight solutions of orange, red, black, and white, four solutions of blue and green.
56 solutions (14 normalized solutions) are permutations of 28 solutions of orange, red, blue, black, and white, one solution of green.
There are a total of 416 solutions (104 normalized solutions) that are permutations, leaving 48 mix solutions.
26 patterns are a combination of two smaller patterns.
24 patterns are a combination of three smaller patterns.
Six patterns are a mix patterns.
There are two minimal touching patterns, which are suboptimal with two extra.
There are ten maximal touching patterns.
The patterns are:

218 normalized solutions are not symmetric in any direction.
48 solutions (12 normalized solutions) are permutations of eight solutions of orange, yellow, blue, and white, one solution of black, one solution of green.
32 solutions (eight normalized solutions) are permutations of eight solutions of orange, yellow, blue, and white, two solutions of green and black.
192 solutions (48 normalized solutions) are permutations of 16 solutions of orange, yellow, black, and white, one solution of green, two solutions of blue.
128 solutions (32 normalized solutions) are permutations of 16 solutions of orange, yellow, black, and white, four solutions of blue and green.
288 solutions (72 normalized solutions) are permutations of 144 solutions of orange, yellow, blue, black, and white, one solution of green.
32 solutions (eight normalized solutions) are permutations of eight solutions of orange, yellow, green, black, and white, two solutions of blue.
There are a total of 720 solutions (180 normalized solutions) that are permutations, leaving 152 mix solutions.
70 patterns are a combination of two smaller patterns.
24 patterns are a combination of three smaller patterns.
22 patterns are a mix patterns.
There are six minimal touching patterns, which are suboptimal with two extra.
There are 11 maximal touching patterns.
The patterns are:

## Chinese Wooden Puzzles in 13 by 4

1,396 normalized solutions are not symmetric in any direction.
480 solutions (120 normalized solutions) are permutations of 20 solutions of orange, red, blue, and white, four solutions of yellow and purple, one solution of green.
624 solutions (156 normalized solutions) are permutations of 52 solutions of orange, red, yellow, white, and purple, one solution of green, two solutions of blue.
416 solutions (104 normalized solutions) are permutations of 52 solutions of orange, red, yellow, white, and purple, four solutions of blue and green.
192 solutions (48 normalized solutions) are permutations of 32 solutions of orange, red, yellow, blue, and white, one solution of green, one solution of purple.
2,464 solutions (616 normalized solutions) are permutations of 1,232 solutions of orange, red, yellow, blue, white, and purple, one solution of green.
128 solutions (32 normalized solutions) are permutations of 32 solutions of orange, red, yellow, green, white, and purple, two solutions of blue.
16 solutions (four normalized solutions) are permutations of eight solutions of orange, red, yellow, blue, green, and white, one solution of purple.
There are a total of 4,320 solutions (1,080 normalized solutions) that are permutations, leaving 1,264 mix solutions.
578 patterns are a combination of two smaller patterns.
216 patterns are a combination of three smaller patterns.
200 patterns are a mix patterns.
There are five minimal touching patterns, which are suboptimal with two extra.
There are four maximal touching patterns.
The patterns are:

4,626 normalized solutions are not symmetric in any direction.
64 solutions (16 normalized solutions) are permutations of 16 solutions of red, yellow, black, and purple, two solutions of orange, blue, and white.
480 solutions (120 normalized solutions) are permutations of 20 solutions of orange, red, blue, and white, four solutions of yellow and purple, one solution of black.
640 solutions (160 normalized solutions) are permutations of 20 solutions of orange, red, blue, and white, 16 solutions of yellow, black, and purple.
384 solutions (96 normalized solutions) are permutations of eight solutions of orange, red, black, and white, four solutions of yellow and purple, two solutions of blue.
320 solutions (80 normalized solutions) are permutations of eight solutions of orange, red, black, and white, 20 solutions of yellow, blue, and purple.
384 solutions (96 normalized solutions) are permutations of 24 solutions of orange, blue, black, and white, eight solutions of red, yellow, and purple.
624 solutions (156 normalized solutions) are permutations of 52 solutions of orange, red, yellow, white, and purple, one solution of black, two solutions of blue.
416 solutions (104 normalized solutions) are permutations of 52 solutions of orange, red, yellow, white, and purple, four solutions of blue and black.
192 solutions (48 normalized solutions) are permutations of 32 solutions of orange, red, yellow, blue, and white, one solution of black, one solution of purple.
224 solutions (56 normalized solutions) are permutations of 28 solutions of orange, red, blue, black, and white, four solutions of yellow and purple.
2,464 solutions (616 normalized solutions) are permutations of 1,232 solutions of orange, red, yellow, blue, white, and purple, one solution of black.
1,552 solutions (388 normalized solutions) are permutations of 388 solutions of orange, red, yellow, black, white, and purple, two solutions of blue.
648 solutions (162 normalized solutions) are permutations of 324 solutions of orange, red, yellow, blue, black, and white, one solution of purple.
There are a total of 8,392 solutions (2,098 normalized solutions) that are permutations, leaving 10,112 mix solutions.
1,096 patterns are a combination of two smaller patterns.
240 patterns are a combination of three smaller patterns.
1,861 patterns are a mix patterns.
Too many patterns to display them all.
The one optimal minimal touching pattern is:

438 normalized solutions are not symmetric in any direction.
192 solutions (48 normalized solutions) are permutations of eight solutions of orange, red, black, and white, four solutions of yellow and purple, one solution of green.
312 solutions (78 normalized solutions) are permutations of 52 solutions of orange, red, yellow, white, and purple, one solution of black, one solution of green.
208 solutions (52 normalized solutions) are permutations of 52 solutions of orange, red, yellow, white, and purple, two solutions of green and black.
64 solutions (16 normalized solutions) are permutations of 32 solutions of orange, red, yellow, green, white, and purple, one solution of black.
776 solutions (194 normalized solutions) are permutations of 388 solutions of orange, red, yellow, black, white, and purple, one solution of green.
There are a total of 1,552 solutions (388 normalized solutions) that are permutations, leaving 200 mix solutions.
216 patterns are a combination of two smaller patterns.
96 patterns are a combination of three smaller patterns.
38 patterns are a mix patterns.
There are seven minimal touching patterns, which are suboptimal with two extra.
There are six maximal touching patterns.
The patterns are:

3,540 normalized solutions are not symmetric in any direction.
288 solutions (72 normalized solutions) are permutations of 12 solutions of orange, red, white, and purple, four solutions of blue and green, one solution of black.
288 solutions (72 normalized solutions) are permutations of 12 solutions of orange, red, white, and purple, four solutions of blue and black, one solution of green.
288 solutions (72 normalized solutions) are permutations of 12 solutions of orange, red, white, and purple, two solutions of green and black, two solutions of blue.
384 solutions (96 normalized solutions) are permutations of 12 solutions of orange, red, white, and purple, 16 solutions of blue, green, and black.
240 solutions (60 normalized solutions) are permutations of 20 solutions of orange, red, blue, and white, two solutions of green and black, one solution of purple.
720 solutions (180 normalized solutions) are permutations of 20 solutions of orange, red, blue, and white, 18 solutions of green, black, and purple.
768 solutions (192 normalized solutions) are permutations of eight solutions of orange, red, black, and white, 16 solutions of blue and purple, one solution of green.
192 solutions (48 normalized solutions) are permutations of eight solutions of orange, red, black, and white, four solutions of blue and green, one solution of purple.
512 solutions (128 normalized solutions) are permutations of eight solutions of orange, red, black, and white, 32 solutions of blue, green, and purple.
1,800 solutions (450 normalized solutions) are permutations of 300 solutions of orange, red, blue, white, and purple, one solution of black, one solution of green.
1,200 solutions (300 normalized solutions) are permutations of 300 solutions of orange, red, blue, white, and purple, two solutions of green and black.
192 solutions (48 normalized solutions) are permutations of 16 solutions of orange, red, green, white, and purple, one solution of black, two solutions of blue.
128 solutions (32 normalized solutions) are permutations of 16 solutions of orange, red, green, white, and purple, four solutions of blue and black.
336 solutions (84 normalized solutions) are permutations of 28 solutions of orange, red, black, white, and purple, one solution of green, two solutions of blue.
224 solutions (56 normalized solutions) are permutations of 28 solutions of orange, red, black, white, and purple, four solutions of blue and green.
168 solutions (42 normalized solutions) are permutations of 28 solutions of orange, red, blue, black, and white, one solution of green, one solution of purple.
568 solutions (142 normalized solutions) are permutations of 284 solutions of orange, red, blue, green, white, and purple, one solution of black.
2,944 solutions (736 normalized solutions) are permutations of 1,472 solutions of orange, red, blue, black, white, and purple, one solution of green.
272 solutions (68 normalized solutions) are permutations of 68 solutions of orange, red, green, black, white, and purple, two solutions of blue.
96 solutions (24 normalized solutions) are permutations of 48 solutions of orange, red, blue, green, black, and white, one solution of purple.
There are a total of 11,608 solutions (2,902 normalized solutions) that are permutations, leaving 2,552 mix solutions.
878 patterns are a combination of two smaller patterns.
558 patterns are a combination of three smaller patterns.
144 patterns are a combination of four smaller patterns.
253 patterns are a mix patterns.
Too many patterns to display them all.
The 19 suboptimal (two extra) minimal touching patterns are:

7,394 normalized solutions are not symmetric in any direction.
96 solutions (24 normalized solutions) are permutations of 24 solutions of yellow, green, black, and purple, two solutions of orange, blue, and white.
288 solutions (72 normalized solutions) are permutations of 12 solutions of orange, yellow, white, and purple, four solutions of blue and green, one solution of black.
288 solutions (72 normalized solutions) are permutations of 12 solutions of orange, yellow, white, and purple, four solutions of blue and black, one solution of green.
288 solutions (72 normalized solutions) are permutations of 12 solutions of orange, yellow, white, and purple, two solutions of green and black, two solutions of blue.
384 solutions (96 normalized solutions) are permutations of 12 solutions of orange, yellow, white, and purple, 16 solutions of blue, green, and black.
96 solutions (24 normalized solutions) are permutations of eight solutions of orange, yellow, blue, and white, two solutions of green and black, one solution of purple.
288 solutions (72 normalized solutions) are permutations of eight solutions of orange, yellow, blue, and white, 18 solutions of green, black, and purple.
1,536 solutions (384 normalized solutions) are permutations of 16 solutions of orange, yellow, black, and white, 16 solutions of blue and purple, one solution of green.
384 solutions (96 normalized solutions) are permutations of 16 solutions of orange, yellow, black, and white, four solutions of blue and green, one solution of purple.
1,024 solutions (256 normalized solutions) are permutations of 16 solutions of orange, yellow, black, and white, 32 solutions of blue, green, and purple.
576 solutions (144 normalized solutions) are permutations of 24 solutions of orange, blue, black, and white, four solutions of yellow and purple, one solution of green.
1,920 solutions (480 normalized solutions) are permutations of 320 solutions of orange, yellow, blue, white, and purple, one solution of black, one solution of green.
1,280 solutions (320 normalized solutions) are permutations of 320 solutions of orange, yellow, blue, white, and purple, two solutions of green and black.
288 solutions (72 normalized solutions) are permutations of 24 solutions of orange, yellow, green, white, and purple, one solution of black, two solutions of blue.
192 solutions (48 normalized solutions) are permutations of 24 solutions of orange, yellow, green, white, and purple, four solutions of blue and black.
2,352 solutions (588 normalized solutions) are permutations of 196 solutions of orange, yellow, black, white, and purple, one solution of green, two solutions of blue.
1,568 solutions (392 normalized solutions) are permutations of 196 solutions of orange, yellow, black, white, and purple, four solutions of blue and green.
864 solutions (216 normalized solutions) are permutations of 144 solutions of orange, yellow, blue, black, and white, one solution of green, one solution of purple.
96 solutions (24 normalized solutions) are permutations of eight solutions of orange, yellow, green, black, and white, two solutions of blue, one solution of purple.
256 solutions (64 normalized solutions) are permutations of eight solutions of orange, yellow, green, black, and white, 16 solutions of blue and purple.
656 solutions (164 normalized solutions) are permutations of 328 solutions of orange, yellow, blue, green, white, and purple, one solution of black.
7,184 solutions (1,796 normalized solutions) are permutations of 3,592 solutions of orange, yellow, blue, black, white, and purple, one solution of green.
608 solutions (152 normalized solutions) are permutations of 152 solutions of orange, yellow, green, black, white, and purple, two solutions of blue.
304 solutions (76 normalized solutions) are permutations of 152 solutions of orange, yellow, blue, green, black, and white, one solution of purple.
There are a total of 22,816 solutions (5,704 normalized solutions) that are permutations, leaving 6,760 mix solutions.
1,914 patterns are a combination of two smaller patterns.
1,188 patterns are a combination of three smaller patterns.
216 patterns are a combination of four smaller patterns.
742 patterns are a mix patterns.
Too many patterns to display them all.
The 16 suboptimal (one extra) minimal touching patterns are:

## Chinese Wooden Puzzles in 14 by 4

283 normalized solutions are not symmetric in any direction.
192 solutions (48 normalized solutions) are permutations of 32 solutions of orange, red, yellow, blue, and white, one solution of black, one solution of green.
128 solutions (32 normalized solutions) are permutations of 32 solutions of orange, red, yellow, blue, and white, two solutions of green and black.
16 solutions (four normalized solutions) are permutations of eight solutions of orange, red, yellow, blue, green, and white, one solution of black.
648 solutions (162 normalized solutions) are permutations of 324 solutions of orange, red, yellow, blue, black, and white, one solution of green.
There are a total of 984 solutions (246 normalized solutions) that are permutations, leaving 148 mix solutions.
158 patterns are a combination of two smaller patterns.
48 patterns are a combination of three smaller patterns.
26 patterns are a mix patterns.
There are five minimal touching patterns, which are suboptimal with two extra.
There are 31 maximal touching patterns.
The patterns are:

## Chinese Wooden Puzzles in 15 by 4

19,650 normalized solutions are not symmetric in any direction.
960 solutions (240 normalized solutions) are permutations of 20 solutions of orange, red, blue, and white, two solutions of green and black, four solutions of yellow and purple.
1,920 solutions (480 normalized solutions) are permutations of 20 solutions of orange, red, blue, and white, 16 solutions of yellow, black, and purple, one solution of green.
960 solutions (240 normalized solutions) are permutations of 20 solutions of orange, red, blue, and white, 24 solutions of yellow, green, black, and purple.
768 solutions (192 normalized solutions) are permutations of eight solutions of orange, red, black, and white, four solutions of blue and green, four solutions of yellow and purple.
960 solutions (240 normalized solutions) are permutations of eight solutions of orange, red, black, and white, 20 solutions of yellow, blue, and purple, one solution of green.
1,152 solutions (288 normalized solutions) are permutations of eight solutions of orange, red, black, and white, 72 solutions of yellow, blue, green, and purple.
1,152 solutions (288 normalized solutions) are permutations of 24 solutions of orange, blue, black, and white, eight solutions of red, yellow, and purple, one solution of green.
16 solutions (four normalized solutions) are permutations of four solutions of red, yellow, green, black, and purple, two solutions of orange, blue, and white.
1,248 solutions (312 normalized solutions) are permutations of 52 solutions of orange, red, yellow, white, and purple, four solutions of blue and green, one solution of black.
1,248 solutions (312 normalized solutions) are permutations of 52 solutions of orange, red, yellow, white, and purple, four solutions of blue and black, one solution of green.
1,248 solutions (312 normalized solutions) are permutations of 52 solutions of orange, red, yellow, white, and purple, two solutions of green and black, two solutions of blue.
1,664 solutions (416 normalized solutions) are permutations of 52 solutions of orange, red, yellow, white, and purple, 16 solutions of blue, green, and black.
384 solutions (96 normalized solutions) are permutations of 32 solutions of orange, red, yellow, blue, and white, two solutions of green and black, one solution of purple.
1,152 solutions (288 normalized solutions) are permutations of 32 solutions of orange, red, yellow, blue, and white, 18 solutions of green, black, and purple.
672 solutions (168 normalized solutions) are permutations of 28 solutions of orange, red, blue, black, and white, four solutions of yellow and purple, one solution of green.
7,392 solutions (1,848 normalized solutions) are permutations of 1,232 solutions of orange, red, yellow, blue, white, and purple, one solution of black, one solution of green.
4,928 solutions (1,232 normalized solutions) are permutations of 1,232 solutions of orange, red, yellow, blue, white, and purple, two solutions of green and black.
384 solutions (96 normalized solutions) are permutations of 32 solutions of orange, red, yellow, green, white, and purple, one solution of black, two solutions of blue.
256 solutions (64 normalized solutions) are permutations of 32 solutions of orange, red, yellow, green, white, and purple, four solutions of blue and black.
4,656 solutions (1,164 normalized solutions) are permutations of 388 solutions of orange, red, yellow, black, white, and purple, one solution of green, two solutions of blue.
3,104 solutions (776 normalized solutions) are permutations of 388 solutions of orange, red, yellow, black, white, and purple, four solutions of blue and green.
48 solutions (12 normalized solutions) are permutations of eight solutions of orange, red, yellow, blue, green, and white, one solution of black, one solution of purple.
1,944 solutions (486 normalized solutions) are permutations of 324 solutions of orange, red, yellow, blue, black, and white, one solution of green, one solution of purple.
384 solutions (96 normalized solutions) are permutations of 48 solutions of orange, red, blue, green, black, and white, four solutions of yellow and purple.
2,528 solutions (632 normalized solutions) are permutations of 1,264 solutions of orange, red, yellow, blue, green, white, and purple, one solution of black.
20,224 solutions (5,056 normalized solutions) are permutations of 10,112 solutions of orange, red, yellow, blue, black, white, and purple, one solution of green.
800 solutions (200 normalized solutions) are permutations of 200 solutions of orange, red, yellow, green, black, white, and purple, two solutions of blue.
296 solutions (74 normalized solutions) are permutations of 148 solutions of orange, red, yellow, blue, green, black, and white, one solution of purple.
There are a total of 62,448 solutions (15,612 normalized solutions) that are permutations, leaving 16,152 mix solutions.
6,002 patterns are a combination of two smaller patterns.
3,948 patterns are a combination of three smaller patterns.
960 patterns are a combination of four smaller patterns.
2,053 patterns are a mix patterns.
Too many patterns to display them all.
The four suboptimal (one extra) minimal touching patterns are:

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