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|-
 
|-
 
!1
 
!1
−
|x    
+
|2    
 
|1   
 
|1   
 
|1x2  
 
|1x2  
 
|-
 
|-
 
!2
 
!2
−
|x    
+
|8    
 
|1   
 
|1   
 
|2x4  
 
|2x4  
 
|-
 
|-
 
!3
 
!3
−
|x
+
|20
 
|1
 
|1
 
|4x5
 
|4x5
 
|-
 
|-
 
!4
 
!4
−
|x
+
|40
 
|2
 
|2
 
|4x10, 5x8
 
|4x10, 5x8
 
|-
 
|-
 
!5
 
!5
 +
|70
 
|2
 
|2
 
|5x14, 7x10
 
|5x14, 7x10
 
|-
 
|-
 
!6
 
!6
 +
|112
 
|2
 
|2
 
|7x16, 8x14
 
|7x16, 8x14
 
|-
 
|-
 
!7
 
!7
 +
|168
 
|3
 
|3
 
|7x24, 8x21, 12x14
 
|7x24, 8x21, 12x14
 
|-
 
|-
 
!8
 
!8
 +
|240
 
|4
 
|4
 
|8x30, 10x24, 12x20, 15x16
 
|8x30, 10x24, 12x20, 15x16
 
|-
 
|-
 
!9
 
!9
 +
|330
 
|3
 
|3
 
|10x33, 11x30, 15x22
 
|10x33, 11x30, 15x22
 
|-
 
|-
 
!10
 
!10
 +
|440
 
|3
 
|3
 
|10x44, 11x40, 20x22
 
|10x44, 11x40, 20x22
 
|-
 
|-
 
!11
 
!11
 +
|572
 
|3
 
|3
 
|11x52, 13x44, 22x26
 
|11x52, 13x44, 22x26
 
|-
 
|-
 
!12
 
!12
 +
|728
 
|3
 
|3
 
|13x56, 14x52, 26x28
 
|13x56, 14x52, 26x28
 
|-
 
|-
 
!13
 
!13
 +
|910
 
|2
 
|2
 
|13x70, 26x35
 
|13x70, 26x35
 
|-
 
|-
 
!14
 
!14
 +
|1120
 
|5       
 
|5       
 
|14x80, 16x70, 20x56, 28x40, 32x35
 
|14x80, 16x70, 20x56, 28x40, 32x35
 
|-
 
|-
 
!15
 
!15
 +
|1360
 
|4
 
|4
 
|16x85, 17x80, 20x68, 34x40
 
|16x85, 17x80, 20x68, 34x40
 
|-
 
|-
 
!16
 
!16
 +
|1632
 
|4
 
|4
 
|16x102, 17x96, 32x51, 34x48
 
|16x102, 17x96, 32x51, 34x48
 
|-
 
|-
 
!17
 
!17
 +
|1938
 
|4
 
|4
 
|17x114, 19x102, 34x57 38x51
 
|17x114, 19x102, 34x57 38x51
 
|-
 
|-
 
!18
 
!18
 +
|2280
 
|6
 
|6
 
|19x120, 20x114, 24x95, 30x76, 38x60, 40x57
 
|19x120, 20x114, 24x95, 30x76, 38x60, 40x57
 
|-
 
|-
 
!19
 
!19
 +
|2660
 
|5
 
|5
 
|19x140, 20x133, 28x95, 35x76, 38x70
 
|19x140, 20x133, 28x95, 35x76, 38x70
 
|-
 
|-
 
!20
 
!20
 +
|3080
 
|7
 
|7
 
|20x154, 22x140, 28x110, 35x88, 40x77, 44x70, 55x56
 
|20x154, 22x140, 28x110, 35x88, 40x77, 44x70, 55x56
 
|-
 
|-
 
!21
 
!21
 +
|3542
 
|3
 
|3
 
|22x161, 23x154, 46x77
 
|22x161, 23x154, 46x77
 
|-
 
|-
 
!22
 
!22
 +
|4048
 
|4
 
|4
 
|22x184, 23x176, 44x92, 46x88
 
|22x184, 23x176, 44x92, 46x88
 
|-
 
|-
 
!23
 
!23
 +
|4600
 
|5
 
|5
 
|23x200, 25x184, 40x115, 46x100, 50x92
 
|23x200, 25x184, 40x115, 46x100, 50x92
 
|-
 
|-
 
!24
 
!24
 +
|5200
 
|6
 
|6
 
|25x208, 26x200, 40x130, 50x104, 52x100, 65x80
 
|25x208, 26x200, 40x130, 50x104, 52x100, 65x80
 
|-
 
|-
 
!25
 
!25
 +
|5850
 
|8
 
|8
 
|25x234, 26x225, 30x195, 39x150, 45x130, 50x117, 65x90, 75x78
 
|25x234, 26x225, 30x195, 39x150, 45x130, 50x117, 65x90, 75x78
 
|-
 
|-
 
!26
 
!26
 +
|6552
 
|10
 
|10
 
|26x252, 28x234, 36x182, 39x168, 42x156, 52x126, 56x117, 63x104,72x91, 78x84
 
|26x252, 28x234, 36x182, 39x168, 42x156, 52x126, 56x117, 63x104,72x91, 78x84
 
|-
 
|-
 
!27
 
!27
 +
|7308
 
|7
 
|7
 
|28x261, 29x252, 36x203, 42x174, 58x126, 63x116, 84x87
 
|28x261, 29x252, 36x203, 42x174, 58x126, 63x116, 84x87
 
|-
 
|-
 
!28
 
!28
 +
|8120
 
|7
 
|7
 
|28x290, 29x280, 35x232, 40x203, 56x145, 58x140, 70x116
 
|28x290, 29x280, 35x232, 40x203, 56x145, 58x140, 70x116
 
|-
 
|-
 
!29
 
!29
 +
|8990
 
|4
 
|4
 
|29x310, 31x290, 58x155, 62x145
 
|29x310, 31x290, 58x155, 62x145
 
|-
 
|-
 
!30
 
!30
 +
|9920
 
|6
 
|6
 
|31x320, 32x310, 40x248, 62x160, 64x155, 80x124
 
|31x320, 32x310, 40x248, 62x160, 64x155, 80x124
 
|-
 
|-
 
!31
 
!31
 +
|10912
 
|5
 
|5
 
|31x352, 32x341, 44x248, 62x176, 88x124
 
|31x352, 32x341, 44x248, 62x176, 88x124
 
|-
 
|-
 
!32
 
!32
 +
|11968
 
|6
 
|6
 
|32x374, 34x352, 44x272, 64x187, 68x176, 88x136
 
|32x374, 34x352, 44x272, 64x187, 68x176, 88x136
 
|-
 
|-
 
!33
 
!33
 +
|13090
 
|7       
 
|7       
 
|34x385, 35x374, 55x238, 70x187, 77x170, 85x154, 110x119
 
|34x385, 35x374, 55x238, 70x187, 77x170, 85x154, 110x119
 
|-
 
|-
 
!34
 
!34
 +
|14280
 
|14
 
|14
 
|34x420, 35x408, 40x357, 42x340, 51x280, 56x255, 60x238, 68x210,70x204, 84x170, 85x168, 102x140, 105x136, 119x120
 
|34x420, 35x408, 40x357, 42x340, 51x280, 56x255, 60x238, 68x210,70x204, 84x170, 85x168, 102x140, 105x136, 119x120

Revision as of 23:49, 27 September 2012

Dit is de Almost Squares - pagina.

Introductie

Tiling Almost Squares van orde n (ASn) is het plaatsen van tegels 1x2, 2x3, ... , nx(n+1) in een frame.


Almost Squares in Almost Squares (ASQAS) is een subest van AS waarbij het frame zelf ook een almost-square is. Er zijn precies vijf instanties van ASQAS (1,3,8,20 en34) en ze hebben allemaal oplossingen.


Frames voor Almost Squares

De volgende framedimensies hebben precies genoeg oppervlakte om de tegels te kunnen inpassen, en de smalste van de twee dimensies is nog groot genoeg om de breedste tegel te kunnen passen.

Eligible frames voor Almost Squares n=1...34
n size #Eligible Frames Eligible Frames
1 2 1 1x2
2 8 1 2x4
3 20 1 4x5
4 40 2 4x10, 5x8
5 70 2 5x14, 7x10
6 112 2 7x16, 8x14
7 168 3 7x24, 8x21, 12x14
8 240 4 8x30, 10x24, 12x20, 15x16
9 330 3 10x33, 11x30, 15x22
10 440 3 10x44, 11x40, 20x22
11 572 3 11x52, 13x44, 22x26
12 728 3 13x56, 14x52, 26x28
13 910 2 13x70, 26x35
14 1120 5 14x80, 16x70, 20x56, 28x40, 32x35
15 1360 4 16x85, 17x80, 20x68, 34x40
16 1632 4 16x102, 17x96, 32x51, 34x48
17 1938 4 17x114, 19x102, 34x57 38x51
18 2280 6 19x120, 20x114, 24x95, 30x76, 38x60, 40x57
19 2660 5 19x140, 20x133, 28x95, 35x76, 38x70
20 3080 7 20x154, 22x140, 28x110, 35x88, 40x77, 44x70, 55x56
21 3542 3 22x161, 23x154, 46x77
22 4048 4 22x184, 23x176, 44x92, 46x88
23 4600 5 23x200, 25x184, 40x115, 46x100, 50x92
24 5200 6 25x208, 26x200, 40x130, 50x104, 52x100, 65x80
25 5850 8 25x234, 26x225, 30x195, 39x150, 45x130, 50x117, 65x90, 75x78
26 6552 10 26x252, 28x234, 36x182, 39x168, 42x156, 52x126, 56x117, 63x104,72x91, 78x84
27 7308 7 28x261, 29x252, 36x203, 42x174, 58x126, 63x116, 84x87
28 8120 7 28x290, 29x280, 35x232, 40x203, 56x145, 58x140, 70x116
29 8990 4 29x310, 31x290, 58x155, 62x145
30 9920 6 31x320, 32x310, 40x248, 62x160, 64x155, 80x124
31 10912 5 31x352, 32x341, 44x248, 62x176, 88x124
32 11968 6 32x374, 34x352, 44x272, 64x187, 68x176, 88x136
33 13090 7 34x385, 35x374, 55x238, 70x187, 77x170, 85x154, 110x119
34 14280 14 34x420, 35x408, 40x357, 42x340, 51x280, 56x255, 60x238, 68x210,70x204, 84x170, 85x168, 102x140, 105x136, 119x120


Nog even voor de leuk:


Eligible frames voor Almost Squares n=1...34
n #Eligible Frames Eligible Frame
1000 onbekend 18200x18370
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