POLYOMINO TILINGS

Polyomino Tilings

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P3 9-omino

Area: 9.

Size: 2x7.

Is rectangular: no.

Is convex: yes.

Holes: 0.

Order: 2.

Square order: ≤ 36.

Odd order: ≤ 95.

Prime rectangles: ≥ 7.

Smallest rectangle tilings

Smallest rectangle (2x9):

Smallest known square (18x18):

Smallest known odd rectangles (15x57, 19x45):

Rectangle tilings' solutions count (including symmetric)

Blue number - strongly prime rectangle (which cannot be divided into two or more number of rectangles tileable by this set).

Green number - weakly prime rectangle (which cannot be divided into two rectangles tileable by this set, but which can be divided into three or more rectangles).

Purple number - prime rectangle (unknown if weakly or strongly prime).

Red number - composite rectangle (which can be divided into two rectangles tileable by this set).

Gray number - it is unknown whether rectangle is prime or composite.

Question mark (?) - solution count is unknown.

Click on underlined numbers to view picture with one solution.

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1
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4
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5
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9
0
2
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4
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8
0
16
0
10
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32
0
11
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0
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12
0
0
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0
0
0
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64
0
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13
0
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14
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15
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17
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18
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64
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19
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20
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21
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22
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23
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24
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25
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26
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27
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28
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29
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30
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31
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32
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33
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34
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35
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36
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37
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38
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39
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40
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41
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42
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43
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44
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45
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46
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48
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49
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54
0
64
0
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16777216
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6.87194767×10¹¹
1.56519849×10¹⁴
4.39804651×10¹³
2.35638441×10¹⁶
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55
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60
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61
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63
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64
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65
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66
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67
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68
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69
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70
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71
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72
0
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16777216
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6.87194767×10¹¹
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4.16728177×10¹⁸
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73
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74
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75
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76
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77
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78
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79
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80
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81
0
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134217728
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6.87194767×10¹¹
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82
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83
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?
84
0
0
0
0
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?
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?
?
?
?
85
0
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86
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87
0
0
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0
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?
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88
0
0
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1.75921860×10¹⁴
0
0
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89
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90
0
1024
0
1048576
0
1.07374182×10¹⁰
0
1.09951162×10¹³
3.51843720×10¹⁴
1.12589990×10¹⁶
1.18932118×10¹⁹
1.15292150×10¹⁹
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≥1.84467440×10²⁰
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91
0
0
0
0
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0
0
0
0
0
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?
?
?
?
92
0
0
0
0
0
0
0
0
7.03687441×10¹⁴
0
0
0
0
0
0
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?
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?
?
?
?
93
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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?
?
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?
?
?
?
94
0
0
0
0
0
0
0
0
1.40737488×10¹⁵
0
0
0
0
0
0
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?
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?
?
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?
95
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
?
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?
?
?
?
96
0
0
0
0
0
0
0
0
2.81474976×10¹⁵
0
0
0
0
0
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?
?
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?
?
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?
97
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
?
?
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?
?
?
98
0
0
0
0
0
0
0
0
5.62949953×10¹⁵
0
0
0
0
0
0
?
?
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?
?
?
?
99
0
2048
0
4194304
0
8.58993459×10¹⁰
0
1.75921860×10¹⁴
0
3.60287970×10¹⁷
0
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0
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9.96196237×10¹⁹
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?
100
0
0
0
0
0
0
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0
1.12589990×10¹⁶
0
0
0
0
0
0
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?
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?
?
?
?
101
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0
0
0
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0
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?
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?
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?
?
102
0
0
0
0
0
0
0
0
2.25179981×10¹⁶
0
0
0
0
0
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?
?
≥1
?
?
?
?
103
0
0
0
0
0
0
0
0
0
0
0
0
0
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0
?
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?
104
0
0
0
0
0
0
0
0
4.50359962×10¹⁶
0
0
0
0
0
0
?
?
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?
?
?
?
105
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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?
?
≥1
?
?
≥1
?
106
0
0
0
0
0
0
0
0
9.00719925×10¹⁶
0
0
0
0
0
0
?
?
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?
?
?
?
107
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
?
?
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?
?
?
?
108
0
4096
0
16777216
0
6.87194767×10¹¹
0
2.81474976×10¹⁵
1.80143985×10¹⁷
1.15292150×10¹⁹
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
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≥1
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?
109
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
?
?
≥1
?
?
?
?
110
0
0
0
0
0
0
0
0
3.60287970×10¹⁷
0
0
0
0
0
0
?
?
≥1
?
?
?
?
111
0
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1.84467440×10²⁰
?
?
≥1
?
?
?
?
112
0
0
0
0
0
0
0
0
7.20575940×10¹⁷
0
0
0
0
0
0
?
?
≥1
?
?
?
?
113
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
?
?
≥1
?
?
?
?
114
0
0
0
0
0
0
0
0
1.44115188×10¹⁸
0
0
0
0
0
≥1.84467440×10²⁰
?
?
≥1
?
?
≥1
?
115
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
?
?
≥1
?
?
?
?
116
0
0
0
0
0
0
0
0
2.88230376×10¹⁸
0
0
0
0
0
0
?
?
≥1
?
?
?
?
117
0
8192
0
67108864
0
5.49755813×10¹²
0
4.50359962×10¹⁶
0
≥1.84467440×10²⁰
0
≥1.84467440×10²⁰
0
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
?
118
0
0
0
0
0
0
0
0
5.76460752×10¹⁸
0
0
0
0
0
0
?
?
≥1
?
?
?
?
119
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
?
?
≥1
?
?
?
?
120
0
0
0
0
0
0
0
0
1.15292150×10¹⁹
0
0
0
0
0
≥1.84467440×10²⁰
?
?
≥1
?
?
≥1
?
121
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
?
?
≥1
?
?
?
?
122
0
0
0
0
0
0
0
0
2.30584300×10¹⁹
0
0
0
0
0
0
?
?
≥1
?
?
?
?
123
0
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1.84467440×10²⁰
?
?
≥1
?
?
≥1
?
124
0
0
0
0
0
0
0
0
4.61168601×10¹⁹
0
0
0
0
0
0
?
?
≥1
?
?
?
?
125
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
?
?
≥1
?
?
?
?
126
0
16384
0
268435456
0
4.39804651×10¹³
0
7.20575940×10¹⁷
9.22337203×10¹⁹
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
?
127
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
?
?
≥1
?
?
?
?
128
0
0
0
0
0
0
0
0
≥1.84467440×10²⁰
0
0
0
0
0
0
?
?
≥1
?
?
?
?
129
0
0
0
0
0
0
0
0
0
0
0
0
0
0
≥1.84467440×10²⁰
?
?
≥1
?
?
?
?
130
0
0
0
0
0
0
0
0
≥1.84467440×10²⁰
0
0
0
0
0
0
?
?
≥1
?
?
?
?
131
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
?
?
≥1
?
?
?
?
132
0
0
0
0
0
0
0
0
≥1.84467440×10²⁰
0
0
0
0
0
≥1.84467440×10²⁰
?
?
≥1
?
?
≥1
?
133
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
?
?
≥1
?
?
?
?
134
0
0
0
0
0
0
0
0
≥1.84467440×10²⁰
0
0
0
0
0
0
?
?
≥1
?
?
?
?
135
0
32768
0
1.07374182×10¹⁰
0
3.51843720×10¹⁴
0
1.15292150×10¹⁹
0
≥1.84467440×10²⁰
0
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1.84467440×10²⁰
≥1
≥1
≥1
≥1
≥1
≥1
?
N>0
x
9k
x
9k
x
9k
x
9k
2k
9k
?
?
9k
9k
3k
?
?
?
?
?
?

Reptile tilings' solutions count (including symmetric)

polyomino \ n²
P3 9-omino
1
0
0
0
0
0
0
0

See Also

P2 9-ominoMonominoes and Dominoes