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|-
 
|-
 
!1
 
!1
−
|2    
+
|3    
 
|1   
 
|1   
−
|1x2
+
|onb.
 
|-
 
|-
 
!2
 
!2
−
|8    
+
|11    
 
|1   
 
|1   
−
|2x4
+
|onb.
 
|-
 
|-
 
!3
 
!3
−
|20
+
|26
 
|1
 
|1
−
|4x5
+
|onb.
 
|-
 
|-
 
!4
 
!4
−
|40
+
|50
 
|2
 
|2
−
|4x10, 5x8
+
|onb.
 
|-
 
|-
 
!5
 
!5
−
|70
+
|85
 
|2
 
|2
 
|5x14, 7x10
 
|5x14, 7x10
 
|-
 
|-
 
!6
 
!6
−
|112
+
|133
 
|2
 
|2
 
|7x16, 8x14
 
|7x16, 8x14
 
|-
 
|-
 
!7
 
!7
−
|168
+
|196
 
|3
 
|3
 
|7x24, 8x21, 12x14
 
|7x24, 8x21, 12x14
 
|-
 
|-
 
!8
 
!8
−
|240
+
|276
 
|4
 
|4
 
|8x30, 10x24, 12x20, 15x16
 
|8x30, 10x24, 12x20, 15x16
 
|-
 
|-
 
!9
 
!9
−
|330
+
|375
 
|3
 
|3
 
|10x33, 11x30, 15x22
 
|10x33, 11x30, 15x22
 
|-
 
|-
 
!10
 
!10
−
|440
+
|495
 
|3
 
|3
 
|10x44, 11x40, 20x22
 
|10x44, 11x40, 20x22
 
|-
 
|-
 
!11
 
!11
−
|572
+
|638
 
|3
 
|3
 
|11x52, 13x44, 22x26
 
|11x52, 13x44, 22x26
 
|-
 
|-
 
!12
 
!12
−
|728
+
|806
 
|3
 
|3
 
|13x56, 14x52, 26x28
 
|13x56, 14x52, 26x28
 
|-
 
|-
 
!13
 
!13
−
|910
+
|1001
 
|2
 
|2
 
|13x70, 26x35
 
|13x70, 26x35
 
|-
 
|-
 
!14
 
!14
−
|1120
+
|1225
 
|5       
 
|5       
 
|14x80, 16x70, 20x56, 28x40, 32x35
 
|14x80, 16x70, 20x56, 28x40, 32x35
 
|-
 
|-
 
!15
 
!15
−
|1360
+
|1480
 
|4
 
|4
 
|16x85, 17x80, 20x68, 34x40
 
|16x85, 17x80, 20x68, 34x40
 
|-
 
|-
 
!16
 
!16
−
|1632
+
|1768
 
|4
 
|4
 
|16x102, 17x96, 32x51, 34x48
 
|16x102, 17x96, 32x51, 34x48
 
|-
 
|-
 
!17
 
!17
−
|1938
+
|2091
 
|4
 
|4
 
|17x114, 19x102, 34x57 38x51
 
|17x114, 19x102, 34x57 38x51
 
|-
 
|-
 
!18
 
!18
−
|2280
+
|2451
 
|6
 
|6
 
|19x120, 20x114, 24x95, 30x76, 38x60, 40x57
 
|19x120, 20x114, 24x95, 30x76, 38x60, 40x57
 
|-
 
|-
 
!19
 
!19
−
|2660
+
|2850
 
|5
 
|5
 
|19x140, 20x133, 28x95, 35x76, 38x70
 
|19x140, 20x133, 28x95, 35x76, 38x70
 
|-
 
|-
 
!20
 
!20
−
|3080
+
|3290
 
|7
 
|7
 
|20x154, 22x140, 28x110, 35x88, 40x77, 44x70, 55x56
 
|20x154, 22x140, 28x110, 35x88, 40x77, 44x70, 55x56
 
|-
 
|-
 
!21
 
!21
−
|3542
+
|3773
 
|3
 
|3
 
|22x161, 23x154, 46x77
 
|22x161, 23x154, 46x77
 
|-
 
|-
 
!22
 
!22
−
|4048
+
|4301
 
|4
 
|4
 
|22x184, 23x176, 44x92, 46x88
 
|22x184, 23x176, 44x92, 46x88
 
|-
 
|-
 
!23
 
!23
−
|4600
+
|4876
 
|5
 
|5
 
|23x200, 25x184, 40x115, 46x100, 50x92
 
|23x200, 25x184, 40x115, 46x100, 50x92
 
|-
 
|-
 
!24
 
!24
−
|5200
+
|5500
 
|6
 
|6
 
|25x208, 26x200, 40x130, 50x104, 52x100, 65x80
 
|25x208, 26x200, 40x130, 50x104, 52x100, 65x80
 
|-
 
|-
 
!25
 
!25
−
|5850
+
|6175
 
|8
 
|8
 
|25x234, 26x225, 30x195, 39x150, 45x130, 50x117, 65x90, 75x78
 
|25x234, 26x225, 30x195, 39x150, 45x130, 50x117, 65x90, 75x78
 
|-
 
|-
 
!26
 
!26
−
|6552
+
|6903
 
|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
+
|7686
 
|7
 
|7
 
|28x261, 29x252, 36x203, 42x174, 58x126, 63x116, 84x87
 
|28x261, 29x252, 36x203, 42x174, 58x126, 63x116, 84x87
 
|-
 
|-
 
!28
 
!28
−
|8120
+
|8526
 
|7
 
|7
 
|28x290, 29x280, 35x232, 40x203, 56x145, 58x140, 70x116
 
|28x290, 29x280, 35x232, 40x203, 56x145, 58x140, 70x116
 
|-
 
|-
 
!29
 
!29
−
|8990
+
|9425
 
|4
 
|4
 
|29x310, 31x290, 58x155, 62x145
 
|29x310, 31x290, 58x155, 62x145
 
|-
 
|-
 
!30
 
!30
−
|9920
+
|10385
 
|6
 
|6
 
|31x320, 32x310, 40x248, 62x160, 64x155, 80x124
 
|31x320, 32x310, 40x248, 62x160, 64x155, 80x124
 
|-
 
|-
 
!31
 
!31
−
|10912
+
|11408
 
|5
 
|5
 
|31x352, 32x341, 44x248, 62x176, 88x124
 
|31x352, 32x341, 44x248, 62x176, 88x124
 
|-
 
|-
 
!32
 
!32
−
|11968
+
|12496
 
|6
 
|6
 
|32x374, 34x352, 44x272, 64x187, 68x176, 88x136
 
|32x374, 34x352, 44x272, 64x187, 68x176, 88x136
 
|-
 
|-
 
!33
 
!33
−
|13090
+
|13651
 
|7       
 
|7       
 
|34x385, 35x374, 55x238, 70x187, 77x170, 85x154, 110x119
 
|34x385, 35x374, 55x238, 70x187, 77x170, 85x154, 110x119
 
|-
 
|-
 
!34
 
!34
−
|14280
+
|14875
 
|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 09:57, 28 September 2012

Dit is de Almost Almost Squares - pagina.

Introductie

Tiling Almost Almost Squares van orde n (AASn) is het plaatsen van tegels 1x3, 2x4, ... , nx(n+2) in een frame.

Almost Almost Squares is gerelateerd aan Almost Squares waar bij tegels van nx(n+1) in een frame gepast moeten worden.


Frames voor Almost 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 area #Eligible Frames Eligible Frames
1 3 1 onb.
2 11 1 onb.
3 26 1 onb.
4 50 2 onb.
5 85 2 5x14, 7x10
6 133 2 7x16, 8x14
7 196 3 7x24, 8x21, 12x14
8 276 4 8x30, 10x24, 12x20, 15x16
9 375 3 10x33, 11x30, 15x22
10 495 3 10x44, 11x40, 20x22
11 638 3 11x52, 13x44, 22x26
12 806 3 13x56, 14x52, 26x28
13 1001 2 13x70, 26x35
14 1225 5 14x80, 16x70, 20x56, 28x40, 32x35
15 1480 4 16x85, 17x80, 20x68, 34x40
16 1768 4 16x102, 17x96, 32x51, 34x48
17 2091 4 17x114, 19x102, 34x57 38x51
18 2451 6 19x120, 20x114, 24x95, 30x76, 38x60, 40x57
19 2850 5 19x140, 20x133, 28x95, 35x76, 38x70
20 3290 7 20x154, 22x140, 28x110, 35x88, 40x77, 44x70, 55x56
21 3773 3 22x161, 23x154, 46x77
22 4301 4 22x184, 23x176, 44x92, 46x88
23 4876 5 23x200, 25x184, 40x115, 46x100, 50x92
24 5500 6 25x208, 26x200, 40x130, 50x104, 52x100, 65x80
25 6175 8 25x234, 26x225, 30x195, 39x150, 45x130, 50x117, 65x90, 75x78
26 6903 10 26x252, 28x234, 36x182, 39x168, 42x156, 52x126, 56x117, 63x104,72x91, 78x84
27 7686 7 28x261, 29x252, 36x203, 42x174, 58x126, 63x116, 84x87
28 8526 7 28x290, 29x280, 35x232, 40x203, 56x145, 58x140, 70x116
29 9425 4 29x310, 31x290, 58x155, 62x145
30 10385 6 31x320, 32x310, 40x248, 62x160, 64x155, 80x124
31 11408 5 31x352, 32x341, 44x248, 62x176, 88x124
32 12496 6 32x374, 34x352, 44x272, 64x187, 68x176, 88x136
33 13651 7 34x385, 35x374, 55x238, 70x187, 77x170, 85x154, 110x119
34 14875 14 34x420, 35x408, 40x357, 42x340, 51x280, 56x255, 60x238, 68x210,70x204, 84x170, 85x168, 102x140, 105x136, 119x120


Nog even voor de leuk:


Some frames for very high Slmost Squares
n #Eligible Frames Eligible Frame
1000 onbekend 18200x18370
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