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| + | == Zie ook == | ||
| + | * [[Almost Squares]] | ||
| + | * [[Almost Almost Almost Squares]] | ||
| + | |||
| + | * [[AI-course]] | ||
Revision as of 10:18, 28 September 2012
Dit is de Almost Squares - pagina.
Introductie
Tiling Almost Squares van orde n (ASn) is het plaatsen van tegels 1x2, 2x3, ... , nx(n+1) in een frame.
Almost Squares in Almost Squares (ASQAS) is een subest van AS waarbij het frame zelf ook een almost-square is. Er zijn precies vijf instanties van ASQAS (1,3,8,20 en34) en ze hebben allemaal oplossingen.
Frames voor 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 | 2 | 1 | 1x2 |
| 2 | 8 | 1 | 2x4 |
| 3 | 20 | 1 | 4x5 |
| 4 | 40 | 2 | 4x10, 5x8 |
| 5 | 70 | 2 | 5x14, 7x10 |
| 6 | 112 | 2 | 7x16, 8x14 |
| 7 | 168 | 3 | 7x24, 8x21, 12x14 |
| 8 | 240 | 4 | 8x30, 10x24, 12x20, 15x16 |
| 9 | 330 | 3 | 10x33, 11x30, 15x22 |
| 10 | 440 | 3 | 10x44, 11x40, 20x22 |
| 11 | 572 | 3 | 11x52, 13x44, 22x26 |
| 12 | 728 | 3 | 13x56, 14x52, 26x28 |
| 13 | 910 | 2 | 13x70, 26x35 |
| 14 | 1120 | 5 | 14x80, 16x70, 20x56, 28x40, 32x35 |
| 15 | 1360 | 4 | 16x85, 17x80, 20x68, 34x40 |
| 16 | 1632 | 4 | 16x102, 17x96, 32x51, 34x48 |
| 17 | 1938 | 4 | 17x114, 19x102, 34x57 38x51 |
| 18 | 2280 | 6 | 19x120, 20x114, 24x95, 30x76, 38x60, 40x57 |
| 19 | 2660 | 5 | 19x140, 20x133, 28x95, 35x76, 38x70 |
| 20 | 3080 | 7 | 20x154, 22x140, 28x110, 35x88, 40x77, 44x70, 55x56 |
| 21 | 3542 | 3 | 22x161, 23x154, 46x77 |
| 22 | 4048 | 4 | 22x184, 23x176, 44x92, 46x88 |
| 23 | 4600 | 5 | 23x200, 25x184, 40x115, 46x100, 50x92 |
| 24 | 5200 | 6 | 25x208, 26x200, 40x130, 50x104, 52x100, 65x80 |
| 25 | 5850 | 8 | 25x234, 26x225, 30x195, 39x150, 45x130, 50x117, 65x90, 75x78 |
| 26 | 6552 | 10 | 26x252, 28x234, 36x182, 39x168, 42x156, 52x126, 56x117, 63x104,72x91, 78x84 |
| 27 | 7308 | 7 | 28x261, 29x252, 36x203, 42x174, 58x126, 63x116, 84x87 |
| 28 | 8120 | 7 | 28x290, 29x280, 35x232, 40x203, 56x145, 58x140, 70x116 |
| 29 | 8990 | 4 | 29x310, 31x290, 58x155, 62x145 |
| 30 | 9920 | 6 | 31x320, 32x310, 40x248, 62x160, 64x155, 80x124 |
| 31 | 10912 | 5 | 31x352, 32x341, 44x248, 62x176, 88x124 |
| 32 | 11968 | 6 | 32x374, 34x352, 44x272, 64x187, 68x176, 88x136 |
| 33 | 13090 | 7 | 34x385, 35x374, 55x238, 70x187, 77x170, 85x154, 110x119 |
| 34 | 14280 | 14 | 34x420, 35x408, 40x357, 42x340, 51x280, 56x255, 60x238, 68x210,70x204, 84x170, 85x168, 102x140, 105x136, 119x120 |
Nog even voor de leuk:
| n | #Eligible Frames | Eligible Frame |
|---|---|---|
| 1000 | onbekend | 18200x18370 |