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|4 | |4 | ||
|1 | |1 | ||
| − | | | + | |1x4 |
|- | |- | ||
!2 | !2 | ||
|14 | |14 | ||
| − | | | + | |1 |
| − | | | + | |2x7 |
|- | |- | ||
!3 | !3 | ||
|32 | |32 | ||
| − | | | + | |1 |
| − | | | + | |4x8 |
|- | |- | ||
!4 | !4 | ||
|60 | |60 | ||
| − | | | + | |3 |
| − | | | + | |4x15, 5x12, 6x10 |
|- | |- | ||
!5 | !5 | ||
|100 | |100 | ||
| − | | | + | |2 |
| − | | | + | |5x20, 10x10 |
|- | |- | ||
!6 | !6 | ||
|154 | |154 | ||
| − | | | + | |2 |
| − | | | + | |7x22, 11x14 |
|- | |- | ||
!7 | !7 | ||
|224 | |224 | ||
|2 | |2 | ||
| − | | | + | |7x32, 8x28, 14x16 |
|- | |- | ||
!8 | !8 | ||
|312 | |312 | ||
| − | | | + | |3 |
| − | | | + | |8x39, 12x26, 13x24 |
|- | |- | ||
!9 | !9 | ||
Revision as of 20:30, 3 October 2012
Dit is de Tiling Almost Almost Almost Squares (TAAAS)- pagina.
Introductie
Tiling Almost Almost Squares van orde n (AASn) is het plaatsen van tegels 1x4, 2x5, ... , nx(n+3) in een frame.
Almost 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 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.
| n | area | #Eligible Frames | Eligible Frames |
|---|---|---|---|
| 1 | 4 | 1 | 1x4 |
| 2 | 14 | 1 | 2x7 |
| 3 | 32 | 1 | 4x8 |
| 4 | 60 | 3 | 4x15, 5x12, 6x10 |
| 5 | 100 | 2 | 5x20, 10x10 |
| 6 | 154 | 2 | 7x22, 11x14 |
| 7 | 224 | 2 | 7x32, 8x28, 14x16 |
| 8 | 312 | 3 | 8x39, 12x26, 13x24 |
| 9 | 420 | 5 | 10x420, 12x25, 14x30, 15x28, 20x21 |
| 10 | 550 | 3 | 10x55, 11x50, 22x25 |
| 11 | 704 | 3 | 11x64, 16x44, 22x32 |
| 12 | 884 | 3 | 13x68, 17x52, 26x34 |
| 13 | 1092 | 4 | 13x84, 14x78, 21x52, 28x39 |
| 14 | 1330 | 3 | 14x95, 19x70, 35x38 |
| 15 | 1600 | 5 | 16x100, 20x80, 25x64, 32x50, 40x40 |
| 16 | 1904 | 4 | 16x119, 17x112, 28x68, 34x56 |
| 17 | 2244 | 5 | 17x132, 22x102, 33x68, 34x66, 44x51 |
| 18 | 2622 | 2 | 19x138, 23x114, 38x69, 46x57 |
| 19 | 3040 | 5 | 19x160, 20x152, 32x95, 38x80, 40x76 |
| 20 | 3500 | 5 | 20x175, 25x140, 28x125, 35x100, 50x70 |
| 21 | 4004 | 5 | 22x182, 26x154, 28x143, 44x91, 52x77 |
| 22 | 4554 | 5 | 22x207, 23x198, 33x138, 46x99, 66x69 |
| 23 | 5152 | 5 | 23x224, 28x184, 32x161, 46x112, 56x92 |
| 24 | 5800 | 5 | 25x232, 29x200, 40x145, 50x116, 58x100 |
| 25 | 6500 | 5 | 25x260, 26x250, 50x130, 52x125, 65x100 |
| 26 | 7254 | 2 | 26x279, 31x234, 39x186, 62x117, 78x93 |
| 27 | 8064 | 9 | 28x288, 32x252, 36x224, 42x192, 48x168, 56x144, 64x126, 72x112, 84x96 |
| 28 | 8932 | 5 | 28x319, 29x308, 44x203, 58x154, 77x116 |
| 29 | 9860 | 1 | 29x340, 34x290, 58x170, 68x145, 85x116 |
| 30 | 10850 | 5 | 31x350, 35x310, 50x217, 62x175, 70x155 |
| 31 | 11904 | 7 | 31x384, 32x372, 48x248, 62x192, 64x186, 93x128, 96x124 |
| 32 | 13024 | 5 | 32x407, 37x352, 44x296, 74x176, 88x148 |
| 33 | 14212 | 5 | 34x418, 38x374, 44x323, 68x 209, 76x187 |
| 34 | 15470 | 7 | 34x455, 35x442, 65x238, 70x221, 85x182, 91x170 ,119x130 |