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{| class="wikitable" style="text-align: right; margin-left: 1em; margin-bottom: 1em; font-size: 85%;" | {| class="wikitable" style="text-align: right; margin-left: 1em; margin-bottom: 1em; font-size: 85%;" | ||
| − | |+Eligible frames voor Almost Squares n=1...34 | + | |+Eligible frames voor Almost Almost Squares n=1...34 |
! n | ! n | ||
! area | ! area | ||
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!9 | !9 | ||
|375 | |375 | ||
| − | | | + | |1 |
| − | | | + | |15x25 |
|- | |- | ||
!10 | !10 | ||
|495 | |495 | ||
| − | | | + | |2 |
| − | | | + | |11x45, 15x33 |
|- | |- | ||
!11 | !11 | ||
|638 | |638 | ||
| − | | | + | |2 |
| − | | | + | |11x58, 22x29 |
|- | |- | ||
!12 | !12 | ||
|806 | |806 | ||
| − | | | + | |2 |
| − | | | + | |13x62, 26x31 |
|- | |- | ||
!13 | !13 | ||
|1001 | |1001 | ||
| − | | | + | |1 |
| − | | | + | |13x77 |
|- | |- | ||
!14 | !14 | ||
|1225 | |1225 | ||
| − | | | + | |2 |
| − | | | + | |25x49, 35x35 |
|- | |- | ||
!15 | !15 | ||
|1480 | |1480 | ||
|4 | |4 | ||
| − | | | + | |20x74, 37x40 |
| + | | 20x74: geen. 37x40: 456 incsp. | ||
|- | |- | ||
!16 | !16 | ||
|1768 | |1768 | ||
| − | | | + | |3 |
| − | | | + | |17x104, 26x68, 34x52 |
| + | | 26x68: 3072 oplossingen incsp. | ||
|- | |- | ||
!17 | !17 | ||
|2091 | |2091 | ||
| − | | | + | |2 |
| − | | | + | |17x123, 41x51 |
| + | |Geen oplossingen. | ||
|- | |- | ||
!18 | !18 | ||
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|2850 | |2850 | ||
|5 | |5 | ||
| − | | | + | |19x150, 25x114, 30x95, 38x75, 50x57 |
|- | |- | ||
!20 | !20 | ||
|3290 | |3290 | ||
| − | | | + | |2 |
|35x94, 47x70 | |35x94, 47x70 | ||
|- | |- | ||
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!28 | !28 | ||
|8526 | |8526 | ||
| − | | | + | |3 |
|49x174, 58x147, 87x98 | |49x174, 58x147, 87x98 | ||
|- | |- | ||
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|3 | |3 | ||
|35x425, 85x175 ,119x125 | |35x425, 85x175 ,119x125 | ||
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|} | |} | ||
Latest revision as of 21:35, 17 October 2012
Dit is de Almost Almost Squares - pagina.
Introductie
Tiling Almost Almost Squares van orde n (AASn) is het plaatsen van tegels 1x3, 2x4, ... , nx(n+2) in een frame.
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 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 | 3 | 1 | 1x3 | |
| 2 | 11 | 0 | none | |
| 3 | 26 | 0 | none | |
| 4 | 50 | 1 | 5x10 | |
| 5 | 85 | 1 | 5x17 | |
| 6 | 133 | 1 | 7x19 | |
| 7 | 196 | 2 | 7x28, 14x14 | |
| 8 | 276 | 1 | 12x23 | |
| 9 | 375 | 1 | 15x25 | |
| 10 | 495 | 2 | 11x45, 15x33 | |
| 11 | 638 | 2 | 11x58, 22x29 | |
| 12 | 806 | 2 | 13x62, 26x31 | |
| 13 | 1001 | 1 | 13x77 | |
| 14 | 1225 | 2 | 25x49, 35x35 | |
| 15 | 1480 | 4 | 20x74, 37x40 | 20x74: geen. 37x40: 456 incsp. |
| 16 | 1768 | 3 | 17x104, 26x68, 34x52 | 26x68: 3072 oplossingen incsp. |
| 17 | 2091 | 2 | 17x123, 41x51 | Geen oplossingen. |
| 18 | 2451 | 2 | 19x129, 43x57 | |
| 19 | 2850 | 5 | 19x150, 25x114, 30x95, 38x75, 50x57 | |
| 20 | 3290 | 2 | 35x94, 47x70 | |
| 21 | 3773 | 1 | 49x77 | |
| 22 | 4301 | 1 | 23x187 | |
| 23 | 4876 | 3 | 23x112, 46x106, 53x92 | |
| 24 | 5500 | 4 | 25x220, 44x125, 50x110, 55x100 | |
| 25 | 6175 | 2 | 25x247, 65x95 | |
| 26 | 6903 | 2 | 39x177, 59x117 | |
| 27 | 7686 | 3 | 42x183, 61x126, 63x122 | |
| 28 | 8526 | 3 | 49x174, 58x147, 87x98 | |
| 29 | 9425 | 1 | 65x145 | |
| 30 | 10385 | 2 | 31x335, 67x155 | |
| 31 | 11408 | 4 | 31x368, 46x248, 62x184, 92x124 | |
| 32 | 12496 | 3 | 44x284, 76x176, 88x142 | |
| 33 | 13651 | 1 | 73x187 | |
| 34 | 14875 | 3 | 35x425, 85x175 ,119x125 |