MeesterDaan (talk | contribs) m (→Frames voor Almost Almost Almost Squares) |
MeesterDaan (talk | contribs) m (→Frames voor Almost Almost Almost Squares) |
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| Line 23: | Line 23: | ||
|4 | |4 | ||
|1 | |1 | ||
| − | |1x4 | + | |1x4, 2x2 |
| + | |1 Trivial solution. | ||
|- | |- | ||
!2 | !2 | ||
| Line 29: | Line 30: | ||
|1 | |1 | ||
|2x7 | |2x7 | ||
| + | |No solutions. | ||
|- | |- | ||
!3 | !3 | ||
| Line 34: | Line 36: | ||
|1 | |1 | ||
|4x8 | |4x8 | ||
| + | |No solutions. | ||
|- | |- | ||
!4 | !4 | ||
| Line 39: | Line 42: | ||
|3 | |3 | ||
|4x15, 5x12, 6x10 | |4x15, 5x12, 6x10 | ||
| + | |No solutions. | ||
|- | |- | ||
!5 | !5 | ||
| Line 44: | Line 48: | ||
|2 | |2 | ||
|5x20, 10x10 | |5x20, 10x10 | ||
| + | |7x22, 11x14 | ||
|- | |- | ||
!6 | !6 | ||
| Line 49: | Line 54: | ||
|2 | |2 | ||
|7x22, 11x14 | |7x22, 11x14 | ||
| + | |No solutions. | ||
|- | |- | ||
!7 | !7 | ||
| Line 54: | Line 60: | ||
|2 | |2 | ||
|7x32, 8x28, 14x16 | |7x32, 8x28, 14x16 | ||
| + | |No solutions. | ||
|- | |- | ||
!8 | !8 | ||
| Line 113: | Line 120: | ||
|5 | |5 | ||
|17x132, 22x102, 33x68, 34x66, 44x51 | |17x132, 22x102, 33x68, 34x66, 44x51 | ||
| + | |33x68: 4 solutions, 34x66: 65 solutions, 44x51: 1132 solutions | ||
|- | |- | ||
!18 | !18 | ||
Revision as of 00:08, 16 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 | 7x22, 11x14 |
| 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 | Two solutions 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 | About 10 solutions for the largest frame, no solutions for other frames. |
| 17 | 2244 | 5 | 17x132, 22x102, 33x68, 34x66, 44x51 | 33x68: 4 solutions, 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:
AS-4208 heeft een vierkant frame (157655x157655);
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)