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Difference between revisions of "Puzzle piece shapes"

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{{Languages}}
 
{{DISPLAYTITLE:Puzzle piece shapes}}
 
{{DISPLAYTITLE:Puzzle piece shapes}}
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==Division of the piece shapes of normal puzzles==
 +
 
 +
A normal puzzle with grid or strip cut consists of pieces with 4 sides and bulges or notches and more or less straight edges, including the edge pieces.
 +
 
 +
==Theoretically possible shapes==
 +
For the consistent division of the edge of the pieces, the following classification will be used:
 +
 
 +
0: the side of the piece has an notch (hole)
 +
 
 +
1: the side of the piece has a bulge (nose)
 +
 
 +
2: the side of the pice is neither 0 nor 1 (straight edge or similar)
 +
 
 +
According to this classification, there can be a total of 3<sup>4</sup> = 81 different pieces. The usual puzzles nowadays have about 5 to 15 different part shapes (not including rotations).
 +
 
 +
==Glossary==
 +
To define a unique notation, the following rule is used:
 +
 
 +
- Each side of a puzzle piece is given the number 0, 1 or 2 according to the notation above.
 +
 
 +
- Starting at 12 clockwise, each side of the piece gets this number and thus each puzzle piece gets a 4-digit number.
 +
 
 +
Example: The puzzle piece 2101 looks like this:
 +
[[File:Teil2101solo.jpg|none|thumb]]
 +
 
 +
{| class="wikitable" style="text-align:center"
 +
|+Glossary of puzzle pieces
 +
|-
 +
! Piece No. !! Digits !! Edge<br>top !! Edge<br>right !! Edge<br>bottom !! Edge<br>left !! Examples
 +
|-
 +
! 1 || 0000
 +
| 0 || 0 || 0 || 0 ||[[File:Teil0000.jpg|none|thumb]]
 +
|-
 +
! 2 || 0001
 +
| 0 || 0 || 0 || 1 ||[[File:Teil0001.jpg|none|thumb]]
 +
|-
 +
! 3 || 0002
 +
| 0 || 0 || 0 || 2 ||[[File:Teil0002.jpg|none|thumb]]
 +
|-
 +
! 4 || 0010
 +
| 0 || 0 || 1 || 0 ||[[File:Teil0010.jpg|none|thumb]]
 +
|-
 +
! 5 || 0011
 +
| 0 || 0 || 1 || 1 ||[[File:Teil0011.jpg|none|thumb]]
 +
|-
 +
! 6 || 0012
 +
| 0 || 0 || 1 || 2 ||[[File:Teil0012.jpg|none|thumb]]
 +
|-
 +
! 7 || 0020
 +
| 0 || 0 || 2 || 0 ||[[File:Teil0020.jpg|none|thumb]]
 +
|-
 +
! 8 || 0021
 +
| 0 || 0 || 2 || 1 ||[[File:Teil0021.jpg|none|thumb]]
 +
|-
 +
! 9 || 0022
 +
| 0 || 0 || 2 || 2 ||[[File:Teil0022.jpg|none|thumb]]
 +
|-
 +
! 10 || 0100
 +
| 0 || 1 || 0 || 0 ||[[File:Teil0100.jpg|none|thumb]]
 +
|-
 +
! 11 || 0101
 +
| 0 || 1 || 0 || 1 ||[[File:Teil0101.jpg|none|thumb]]
 +
|-
 +
! 12 || 0102
 +
| 0 || 1 || 0 || 2 ||[[File:Teil0102.jpg|none|thumb]]
 +
|-
 +
! 13 || 0110
 +
| 0 || 1 || 1 || 0 ||[[File:Teil0110.jpg|none|thumb]]
 +
|-
 +
! 14 || 0111
 +
| 0 || 1 || 1 || 1 ||[[File:Teil0111.jpg|none|thumb]]
 +
|-
 +
! 15 || 0112
 +
| 0 || 1 || 1 || 2 ||[[File:Teil0112.jpg|none|thumb]]
 +
|-
 +
! 16 || 0120
 +
| 0 || 1 || 2 || 0 ||[[File:Teil0120.jpg|none|thumb]]
 +
|-
 +
! 17 || 0121
 +
| 0 || 1 || 2 || 1 ||[[File:Teil0121.jpg|none|thumb]]
 +
|-
 +
! 18 || 0122
 +
| 0 || 1 || 2 || 2 ||[[File:Teil0122.jpg|none|thumb]]
 +
|-
 +
! 19 || 0200
 +
| 0 || 2 || 0 || 0 ||[[File:Teil0200.jpg|none|thumb]]
 +
|-
 +
! 20 || 0201
 +
| 0 || 2 || 0 || 1 ||[[File:Teil0201.jpg|none|thumb]]
 +
|-
 +
! 21 || 0202
 +
| 0 || 2 || 0 || 2 ||[[File:Teil0202.jpg|none|thumb]]
 +
|-
 +
! 22 || 0210
 +
| 0 || 2 || 1 || 0 ||[[File:Teil0210.jpg|none|thumb]]
 +
|-
 +
! 23 || 0211
 +
| 0 || 2 || 1 || 1 ||[[File:Teil0211.jpg|none|thumb]]
 +
|-
 +
! 24 || 0212
 +
| 0 || 2 || 1 || 2 ||[[File:Teil0212.jpg|none|thumb]]
 +
|-
 +
! 25 || 0220
 +
| 0 || 2 || 2 || 0 ||[[File:Teil0220.jpg|none|thumb]]
 +
|-
 +
! 26 || 0221
 +
| 0 || 2 || 2 || 1 ||[[File:Teil0221.jpg|none|thumb]]
 +
|-
 +
! 27|| 0222
 +
| 0 || 2 || 2 || 2 ||[[File:Teil0222.jpg|none|thumb]]
 +
|-
 +
! 28 || 1000
 +
| 1 || 0 || 0 || 0 ||[[File:Teil1000.jpg|none|thumb]]
 +
|-
 +
! 29 || 1001
 +
| 1 || 0 || 0 || 1 ||[[File:Teil1001.jpg|none|thumb]]
 +
|-
 +
! 30 || 1002
 +
| 1 || 0 || 0 || 2 ||[[File:Teil1002.jpg|none|thumb]]
 +
|-
 +
! 31 || 1010
 +
| 1 || 0 || 1 || 0 ||[[File:Teil1010.jpg|none|thumb]]
 +
|-
 +
! 32 || 1011
 +
| 1 || 0 || 1 || 1 ||[[File:Teil1011.jpg|none|thumb]]
 +
|-
 +
! 33 || 1012
 +
| 1 || 0 || 1 || 2 ||[[File:Teil1012.jpg|none|thumb]]
 +
|-
 +
! 34 || 1020
 +
| 1 || 0 || 2 || 0 ||[[File:Teil1020.jpg|none|thumb]]
 +
|-
 +
! 35 || 1021
 +
| 1 || 0 || 2 || 1 ||[[File:Teil1021.jpg|none|thumb]]
 +
|-
 +
! 36 || 1022
 +
| 1 || 0 || 2 || 2 ||[[File:Teil1022.jpg|none|thumb]]
 +
|-
 +
! 37 || 1100
 +
| 1 || 1 || 0 || 0 ||[[File:Teil1100.jpg|none|thumb]]
 +
|-
 +
! 38 || 1101
 +
| 1 || 1 || 0 || 1 ||[[File:Teil1101.jpg|none|thumb]]
 +
|-
 +
! 39 || 1102
 +
| 1 || 1 || 0 || 2 ||[[File:Teil1102.jpg|none|thumb]]
 +
|-
 +
! 40 || 1110
 +
| 1 || 1 || 1 || 0 ||[[File:Teil1110.jpg|none|thumb]]
 +
|-
 +
! 41 || 1111
 +
| 1 || 1 || 1 || 1 ||[[File:Teil1111.jpg|none|thumb]]
 +
|-
 +
! 42 || 1112
 +
| 1 || 1 || 1 || 2 ||[[File:Teil1112.jpg|none|thumb]]
 +
|-
 +
! 43 || 1120
 +
| 1 || 1 || 2 || 0 ||[[File:Teil1120.jpg|none|thumb]]
 +
|-
 +
! 44 || 1121
 +
| 1 || 1 || 2 || 1 ||[[File:Teil1121.jpg|none|thumb]]
 +
|-
 +
! 45 || 1122
 +
| 1 || 1 || 2 || 2 ||[[File:Teil1122.jpg|none|thumb]]
 +
|-
 +
! 46 || 1200
 +
| 1 || 2 || 0 || 0 ||[[File:Teil1200.jpg|none|thumb]]
 +
|-
 +
! 47 || 1201
 +
| 1 || 2 || 0 || 1 ||[[File:Teil1201.jpg|none|thumb]]
 +
|-
 +
! 48 || 1202
 +
| 1 || 2 || 0 || 2 ||[[File:Teil1202.jpg|none|thumb]]
 +
|-
 +
! 49 || 1210
 +
| 1 || 2 || 1 || 0 ||[[File:Teil1210.jpg|none|thumb]]
 +
|-
 +
! 50 || 1211
 +
| 1 || 2 || 1 || 1 ||[[File:Teil1211.jpg|none|thumb]]
 +
|-
 +
! 51 || 1212
 +
| 1 || 2 || 1 || 2 ||[[File:Teil1212.jpg|none|thumb]]
 +
|-
 +
! 52 || 1220
 +
| 1 || 2 || 2 || 0 ||[[File:Teil1220.jpg|none|thumb]]
 +
|-
 +
! 53 || 1221
 +
| 1 || 2 || 2 || 1 ||[[File:Teil1221.jpg|none|thumb]]
 +
|-
 +
! 54 || 1222
 +
| 1 || 2 || 2 || 2 ||[[File:Teil1222.jpg|none|thumb]]
 +
|-
 +
! 55 || 2000
 +
| 2 || 0 || 0 || 0 ||[[File:Teil2000.jpg|none|thumb]]
 +
|-
 +
! 56 || 2001
 +
| 2 || 0 || 0 || 1 ||[[File:Teil2001.jpg|none|thumb]]
 +
|-
 +
! 57 || 2002
 +
| 2 || 0 || 0 || 2 ||[[File:Teil2002.jpg|none|thumb]]
 +
|-
 +
! 58 || 2010
 +
| 2 || 0 || 1 || 0 ||[[File:Teil2010.jpg|none|thumb]]
 +
|-
 +
! 59 || 2011
 +
| 2 || 0 || 1 || 1 ||[[File:Teil2011.jpg|none|thumb]]
 +
|-
 +
! 60 || 2012
 +
| 2 || 0 || 1 || 2 ||[[File:Teil2012.jpg|none|thumb]]
 +
|-
 +
! 61 || 2020
 +
| 2 || 0 || 2 || 0 ||[[File:Teil2020.jpg|none|thumb]]
 +
|-
 +
! 62|| 2021
 +
| 2 || 0 || 2 || 1 ||[[File:Teil2021.jpg|none|thumb]]
 +
|-
 +
! 63 || 2022
 +
| 2 || 0 || 2 || 2 ||[[File:Teil2022.jpg|none|thumb]]
 +
|-
 +
! 64|| 2100
 +
| 2 || 1 || 0 || 0 ||[[File:Teil2100.jpg|none|thumb]]
 +
|-
 +
! 65 || 2101
 +
| 2 || 1 || 0 || 1 ||[[File:Teil2101.jpg|none|thumb]]
 +
|-
 +
! 66 || 2102
 +
| 2 || 1 || 0 || 2 ||[[File:Teil2102.jpg|none|thumb]]
 +
|-
 +
! 67 || 2110
 +
| 2 || 1 || 1 || 0 ||[[File:Teil2110.jpg|none|thumb]]
 +
|-
 +
! 68 || 2111
 +
| 2 || 1 || 1 || 1 ||[[File:Teil2111.jpg|none|thumb]]
 +
|-
 +
! 69 || 2112
 +
| 2 || 1 || 1 || 2 ||[[File:Teil2112.jpg|none|thumb]]
 +
|-
 +
! 70 || 2120
 +
| 2 || 1 || 2 || 0 ||[[File:Teil2120.jpg|none|thumb]]
 +
|-
 +
! 71 || 2121
 +
| 2 || 1 || 2 || 1 ||[[File:Teil2121.jpg|none|thumb]]
 +
|-
 +
! 72 || 2122
 +
| 2 || 1 || 2 || 2 ||[[File:Teil2122.jpg|none|thumb]]
 +
|-
 +
! 73 || 2200
 +
| 2 || 2 || 0 || 0 ||[[File:Teil2200.jpg|none|thumb]]
 +
|-
 +
! 74 || 2201
 +
| 2 || 2 || 0 || 1 ||[[File:Teil2201.jpg|none|thumb]]
 +
|-
 +
! 75 || 2202
 +
| 2 || 2 || 0 || 2 ||[[File:Teil2202.jpg|none|thumb]]
 +
|-
 +
! 76 || 2210
 +
| 2 || 2 || 1 || 0 ||[[File:Teil2210.jpg|none|thumb]]
 +
|-
 +
! 77 || 2211
 +
| 2 || 2 || 1 || 1 ||[[File:Teil2211.jpg|none|thumb]]
 +
|-
 +
! 78 || 2212
 +
| 2 || 2 || 1 || 2 ||[[File:Teil2212.jpg|none|thumb]]
 +
|-
 +
! 79 || 2220
 +
| 2 || 2 || 2 || 0 ||[[File:Teil2220.jpg|none|thumb]]
 +
|-
 +
! 80 || 2221
 +
| 2 || 2 || 2 || 1 ||[[File:Teil2221.jpg|none|thumb]]
 +
|-
 +
! 81 || 2222
 +
| 2 || 2 || 2 || 2 ||[[File:Teil2222.jpg|none|thumb]]
 +
|}
 +
 
 +
'''Note:'''
 +
 
 +
1) <s>The piece No. 81 (2222) should not exist, since there is no interlocking connection to the neighboring pieces on any side.</s>
 +
 
 +
Older puzzles have much more different pieces only by the possibilitiy of the piece side "2". The puzzle [[4000 Ramsau, Germany]] of 1974 has even edge pieces with the three other piece sides "2", so that also the piece No. 81 exists.
 +
2) Since the alignment of a piece is clearly fixed first in the finished puzzle, many pieces are equivalent by rotation.
 +
 
 +
Beispiel: Piece No. 14 (0111) is equivalent to piece No. 40 (1110), No. 38 (1101) and No. 32 (1011). This is shown in the next table.
 +
 
 +
==Equivalent piece shapes==
 +
{| class="wikitable" style="text-align:center"
 +
|+Puzzle pieces with rotation
 +
|-
 +
! Piece No. !! equivalent No. !! Examples
 +
|-
 +
! G1
 +
| 1 ||
 +
|-
 +
! G2
 +
| 2, 4, 10, 28 ||
 +
|-
 +
! G3
 +
| 3, 7, 19, 55 ||
 +
|-
 +
! G4
 +
| 5, 13, 37, 29 ||
 +
|-
 +
! G5
 +
| 6, 16, 46, 56 ||
 +
|-
 +
! G6
 +
| 8, 22, 64, 30 ||
 +
|-
 +
! G7
 +
| 9, 25, 73, 57 ||
 +
|-
 +
! G8
 +
| 11, 31 ||
 +
|-
 +
! G9
 +
| 12, 34, 20, 58 ||
 +
|-
 +
! G10
 +
| 14, 40, 38, 32 ||
 +
|-
 +
! G11
 +
| 15, 43, 47, 59 ||
 +
|-
 +
! G12
 +
| 17, 49, 65, 33 ||
 +
|-
 +
! G13
 +
| 18, 52, 74, 60 ||
 +
|-
 +
! G14
 +
| 21, 61 ||
 +
|-
 +
! G15
 +
| 23, 67, 39, 35 ||
 +
|-
 +
! G16
 +
| 24, 70, 48, 62 ||
 +
|-
 +
! G17
 +
| 26, 76, 66, 36 ||
 +
|-
 +
! G18
 +
| 27, 79, 75, 63 ||
 +
|-
 +
! G19
 +
| 41 ||
 +
|-
 +
! G20
 +
| 42, 44, 50, 68 ||
 +
|-
 +
! G21
 +
| 45, 53, 77, 69 ||
 +
|-
 +
! G22
 +
| 51, 71 ||
 +
|-
 +
! G23
 +
| 54, 80, 78, 72 ||
 +
|-
 +
! G24
 +
| 81 ||
 +
|}
 +
 
 
[[Category:Puzzle information]]
 
[[Category:Puzzle information]]

Revision as of 09:26, 10 April 2017

Language: English  • Deutsch

Division of the piece shapes of normal puzzles

A normal puzzle with grid or strip cut consists of pieces with 4 sides and bulges or notches and more or less straight edges, including the edge pieces.

Theoretically possible shapes

For the consistent division of the edge of the pieces, the following classification will be used:

0: the side of the piece has an notch (hole)

1: the side of the piece has a bulge (nose)

2: the side of the pice is neither 0 nor 1 (straight edge or similar)

According to this classification, there can be a total of 34 = 81 different pieces. The usual puzzles nowadays have about 5 to 15 different part shapes (not including rotations).

Glossary

To define a unique notation, the following rule is used:

- Each side of a puzzle piece is given the number 0, 1 or 2 according to the notation above.

- Starting at 12 clockwise, each side of the piece gets this number and thus each puzzle piece gets a 4-digit number.

Example: The puzzle piece 2101 looks like this:

Teil2101solo.jpg
Glossary of puzzle pieces
Piece No. Digits Edge
top		 Edge
right		 Edge
bottom		 Edge
left		 Examples
1 0000 0 0 0 0
Teil0000.jpg
2 0001 0 0 0 1
Teil0001.jpg
3 0002 0 0 0 2
Teil0002.jpg
4 0010 0 0 1 0
Teil0010.jpg
5 0011 0 0 1 1
Teil0011.jpg
6 0012 0 0 1 2
Teil0012.jpg
7 0020 0 0 2 0
Teil0020.jpg
8 0021 0 0 2 1
Teil0021.jpg
9 0022 0 0 2 2
Teil0022.jpg
10 0100 0 1 0 0
Teil0100.jpg
11 0101 0 1 0 1
Teil0101.jpg
12 0102 0 1 0 2
Teil0102.jpg
13 0110 0 1 1 0
Teil0110.jpg
14 0111 0 1 1 1
Teil0111.jpg
15 0112 0 1 1 2
Teil0112.jpg
16 0120 0 1 2 0
Teil0120.jpg
17 0121 0 1 2 1
Teil0121.jpg
18 0122 0 1 2 2
Teil0122.jpg
19 0200 0 2 0 0
Teil0200.jpg
20 0201 0 2 0 1
Teil0201.jpg
21 0202 0 2 0 2
Teil0202.jpg
22 0210 0 2 1 0
Teil0210.jpg
23 0211 0 2 1 1
Teil0211.jpg
24 0212 0 2 1 2
Teil0212.jpg
25 0220 0 2 2 0
Teil0220.jpg
26 0221 0 2 2 1
Teil0221.jpg
27 0222 0 2 2 2
Teil0222.jpg
28 1000 1 0 0 0
Teil1000.jpg
29 1001 1 0 0 1
Teil1001.jpg
30 1002 1 0 0 2
Teil1002.jpg
31 1010 1 0 1 0
Teil1010.jpg
32 1011 1 0 1 1
Teil1011.jpg
33 1012 1 0 1 2
Teil1012.jpg
34 1020 1 0 2 0
Teil1020.jpg
35 1021 1 0 2 1
Teil1021.jpg
36 1022 1 0 2 2
Teil1022.jpg
37 1100 1 1 0 0
Teil1100.jpg
38 1101 1 1 0 1
Teil1101.jpg
39 1102 1 1 0 2
Teil1102.jpg
40 1110 1 1 1 0
Teil1110.jpg
41 1111 1 1 1 1
Teil1111.jpg
42 1112 1 1 1 2
Teil1112.jpg
43 1120 1 1 2 0
Teil1120.jpg
44 1121 1 1 2 1
Teil1121.jpg
45 1122 1 1 2 2
Teil1122.jpg
46 1200 1 2 0 0
Teil1200.jpg
47 1201 1 2 0 1
Teil1201.jpg
48 1202 1 2 0 2
Teil1202.jpg
49 1210 1 2 1 0
Teil1210.jpg
50 1211 1 2 1 1
Teil1211.jpg
51 1212 1 2 1 2
Teil1212.jpg
52 1220 1 2 2 0
Teil1220.jpg
53 1221 1 2 2 1
Teil1221.jpg
54 1222 1 2 2 2
Teil1222.jpg
55 2000 2 0 0 0
Teil2000.jpg
56 2001 2 0 0 1
Teil2001.jpg
57 2002 2 0 0 2
Teil2002.jpg
58 2010 2 0 1 0
Teil2010.jpg
59 2011 2 0 1 1
Teil2011.jpg
60 2012 2 0 1 2
Teil2012.jpg
61 2020 2 0 2 0
Teil2020.jpg
62 2021 2 0 2 1
Teil2021.jpg
63 2022 2 0 2 2
Teil2022.jpg
64 2100 2 1 0 0
Teil2100.jpg
65 2101 2 1 0 1
Teil2101.jpg
66 2102 2 1 0 2
Teil2102.jpg
67 2110 2 1 1 0
Teil2110.jpg
68 2111 2 1 1 1
Teil2111.jpg
69 2112 2 1 1 2
Teil2112.jpg
70 2120 2 1 2 0
Teil2120.jpg
71 2121 2 1 2 1
Teil2121.jpg
72 2122 2 1 2 2
Teil2122.jpg
73 2200 2 2 0 0
Teil2200.jpg
74 2201 2 2 0 1
Teil2201.jpg
75 2202 2 2 0 2
Teil2202.jpg
76 2210 2 2 1 0
Teil2210.jpg
77 2211 2 2 1 1
Teil2211.jpg
78 2212 2 2 1 2
Teil2212.jpg
79 2220 2 2 2 0
Teil2220.jpg
80 2221 2 2 2 1
Teil2221.jpg
81 2222 2 2 2 2
Teil2222.jpg

Note:

1) The piece No. 81 (2222) should not exist, since there is no interlocking connection to the neighboring pieces on any side.

Older puzzles have much more different pieces only by the possibilitiy of the piece side "2". The puzzle 4000 Ramsau, Germany of 1974 has even edge pieces with the three other piece sides "2", so that also the piece No. 81 exists. 2) Since the alignment of a piece is clearly fixed first in the finished puzzle, many pieces are equivalent by rotation.

Beispiel: Piece No. 14 (0111) is equivalent to piece No. 40 (1110), No. 38 (1101) and No. 32 (1011). This is shown in the next table.

Equivalent piece shapes

Puzzle pieces with rotation
Piece No. equivalent No. Examples
G1 1
G2 2, 4, 10, 28
G3 3, 7, 19, 55
G4 5, 13, 37, 29
G5 6, 16, 46, 56
G6 8, 22, 64, 30
G7 9, 25, 73, 57
G8 11, 31
G9 12, 34, 20, 58
G10 14, 40, 38, 32
G11 15, 43, 47, 59
G12 17, 49, 65, 33
G13 18, 52, 74, 60
G14 21, 61
G15 23, 67, 39, 35
G16 24, 70, 48, 62
G17 26, 76, 66, 36
G18 27, 79, 75, 63
G19 41
G20 42, 44, 50, 68
G21 45, 53, 77, 69
G22 51, 71
G23 54, 80, 78, 72
G24 81
Retrieved from "https://www.jigsaw-wiki.com/w/index.php?title=Puzzle_piece_shapes&oldid=78070"