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! #Eligible Frames | ! #Eligible Frames | ||
! Eligible Frames | ! Eligible Frames | ||
| + | ! Remarks | ||
|- | |- | ||
!1 | !1 | ||
| Line 68: | Line 69: | ||
|3 | |3 | ||
|10x55, 11x50, 22x25 | |10x55, 11x50, 22x25 | ||
| + | |No solutions. | ||
|- | |- | ||
!11 | !11 | ||
| Line 73: | Line 75: | ||
|3 | |3 | ||
|11x64, 16x44, 22x32 | |11x64, 16x44, 22x32 | ||
| + | |No solutions. | ||
|- | |- | ||
!12 | !12 | ||
| Line 78: | Line 81: | ||
|3 | |3 | ||
|13x68, 17x52, 26x34 | |13x68, 17x52, 26x34 | ||
| + | |No solutions. | ||
|- | |- | ||
!13 | !13 | ||
| Line 83: | Line 87: | ||
|4 | |4 | ||
|13x84, 14x78, 21x52, 28x39 | |13x84, 14x78, 21x52, 28x39 | ||
| + | |Two solutions for the largest frame, the others have none. | ||
|- | |- | ||
!14 | !14 | ||
| Line 88: | Line 93: | ||
|3 | |3 | ||
|14x95, 19x70, 35x38 | |14x95, 19x70, 35x38 | ||
| + | |No solutions for all frame sizes. | ||
|- | |- | ||
!15 | !15 | ||
| Line 93: | Line 99: | ||
|5 | |5 | ||
|16x100, 20x80, 25x64, 32x50, 40x40 | |16x100, 20x80, 25x64, 32x50, 40x40 | ||
| + | |Many solutions for 40x40, three distinct solutions for 32x50, No solutions for other frame sizes. | ||
|- | |- | ||
!16 | !16 | ||
Revision as of 17:04, 15 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 | |
| 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 | 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 for all frame sizes. |
| 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 | |
| 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 |
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)