MeesterDaan (talk | contribs) m (→vierkante frames) |
MeesterDaan (talk | contribs) (→Frames voor Almost Almost Almost Squares) |
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|4 | |4 | ||
|13x84, 14x78, 21x52, 28x39 | |13x84, 14x78, 21x52, 28x39 | ||
| − | | | + | |Four solutions in 1 bag for the largest frame, the others have none. |
|- | |- | ||
!14 | !14 | ||
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|4 | |4 | ||
|16x119, 17x112, 28x68, 34x56 | |16x119, 17x112, 28x68, 34x56 | ||
| − | | | + | |34x56: 16 solutions (partial retilings) |
|- | |- | ||
!17 | !17 | ||
| Line 120: | Line 120: | ||
|5 | |5 | ||
|17x132, 22x102, 33x68, 34x66, 44x51 | |17x132, 22x102, 33x68, 34x66, 44x51 | ||
| − | |33x68: | + | |33x68: 8 solutions (partial retilings), 34x66: 65 solutions, 44x51: 1132 solutions |
|- | |- | ||
!18 | !18 | ||
Revision as of 23:49, 19 October 2012
Dit is de Tiling Almost Almost Almost Squares (TAAAS)- pagina.
Introductie
Tiling Almost Almost Almost Squares van orde n (AAASn) 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 | Remarks |
|---|---|---|---|---|
| 1 | 4 | 1 | 1x4, 2x2 | 1 Trivial solution. |
| 2 | 14 | 1 | 2x7 | No solutions. |
| 3 | 32 | 1 | 4x8 | No solutions. |
| 4 | 60 | 3 | 4x15, 5x12, 6x10 | No solutions. |
| 5 | 100 | 2 | 5x20, 10x10 | No solutions? |
| 6 | 154 | 2 | 7x22, 11x14 | No solutions. |
| 7 | 224 | 2 | 7x32, 8x28, 14x16 | No solutions. |
| 8 | 312 | 3 | 8x39, 12x26, 13x24 | No solutions. |
| 9 | 420 | 5 | 10x420, 12x35, 14x30, 15x28, 20x21 | No solutions. |
| 10 | 550 | 3 | 10x55, 11x50, 22x25 | No solutions. |
| 11 | 704 | 3 | 11x64, 16x44, 22x32 | No solutions. |
| 12 | 884 | 3 | 13x68, 17x52, 26x34 | No solutions. |
| 13 | 1092 | 4 | 13x84, 14x78, 21x52, 28x39 | Four solutions in 1 bag for the largest frame, the others have none. |
| 14 | 1330 | 3 | 14x95, 19x70, 35x38 | No solutions. |
| 15 | 1600 | 5 | 16x100, 20x80, 25x64, 32x50, 40x40 | Many solutions for 40x40, three distinct solutions for 32x50, No solutions for other frame sizes. |
| 16 | 1904 | 4 | 16x119, 17x112, 28x68, 34x56 | 34x56: 16 solutions (partial retilings) |
| 17 | 2244 | 5 | 17x132, 22x102, 33x68, 34x66, 44x51 | 33x68: 8 solutions (partial retilings), 34x66: 65 solutions, 44x51: 1132 solutions |
| 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 |
vierkante frames
Exact-fit vierkante frames zijn zeer zeldzaam in deze series:
AAS-7 heeft een vierkant frame (14x14) AAS-14 heeft een vierkant frame (35x35) AAS-168 heeft een vierkant frame (1274x1274) AAS-4318 heeft een vierkant frame (163904x163904)
AAAS-1 heeft een vierkanten frame (2x2) AAAS-5 heeft een vierkanten frame (10x10) AAAS-15 heeft een vierkant frame (40x40) AAAS-49 heeft een vierkant frame (210x210)