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2016-12-30, 02:36
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#34 |
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Nov 2016
24 Posts |
Thanks for the note. I've updated a(101).
Any chance you can beat my a(99) = 27? That's my only value under 100 that goes past my upper bound. Another that might be easy to beat is a(60)=18. |
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2016-12-30, 23:55
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#35 | |
"Robert Gerbicz"
Oct 2005
Hungary
22·7·53 Posts |
Quote:
Code:
a(60)<=16 aaaaaaaaaaaaaaaagggggffffffffffffffffffffffffffffffffffbbbbb aaaaaaaaaaaaaaaagggggffffffffffffffffffffffffffffffffffbbbbb aaaaaaaaaaaaaaaagggggffffffffffffffffffffffffffffffffffbbbbb aaaaaaaaaaaaaaaagggggffffffffffffffffffffffffffffffffffbbbbb aaaaaaaaaaaaaaaagggggffffffffffffffffffffffffffffffffffbbbbb aaaaaaaaaaaaaaaagggggffffffffffffffffffffffffffffffffffbbbbb aaaaaaaaaaaaaaaagggggooooooooooooooooooooppppppppjjjjjjbbbbb aaaaaaaaaaaaaaaagggggooooooooooooooooooooppppppppjjjjjjbbbbb aaaaaaaaaaaaaaaagggggooooooooooooooooooooppppppppjjjjjjbbbbb aaaaaaaaaaaaaaaagggggooooooooooooooooooooppppppppjjjjjjbbbbb aaaaaaaaaaaaaaaagggggooooooooooooooooooooppppppppjjjjjjbbbbb aaaaaaaaaaaaaaaagggggooooooooooooooooooooppppppppjjjjjjbbbbb aaaaaaaaaaaaaaaagggggooooooooooooooooooooppppppppjjjjjjbbbbb eeeeeeeeehhhhhhhgggggooooooooooooooooooooppppppppjjjjjjbbbbb eeeeeeeeehhhhhhhgggggooooooooooooooooooooppppppppjjjjjjbbbbb eeeeeeeeehhhhhhhgggggooooooooooooooooooooppppppppjjjjjjbbbbb eeeeeeeeehhhhhhhgggggooooooooooooooooooooppppppppjjjjjjbbbbb eeeeeeeeehhhhhhhgggggnnnnnnqqqqqqqqqqqqqqppppppppjjjjjjbbbbb eeeeeeeeehhhhhhhgggggnnnnnnqqqqqqqqqqqqqqppppppppjjjjjjbbbbb eeeeeeeeehhhhhhhgggggnnnnnnqqqqqqqqqqqqqqppppppppjjjjjjbbbbb eeeeeeeeehhhhhhhgggggnnnnnnqqqqqqqqqqqqqqppppppppjjjjjjbbbbb eeeeeeeeehhhhhhhgggggnnnnnnqqqqqqqqqqqqqqppppppppjjjjjjbbbbb eeeeeeeeehhhhhhhgggggnnnnnnqqqqqqqqqqqqqqppppppppjjjjjjbbbbb eeeeeeeeehhhhhhhgggggnnnnnnqqqqqqqqqqqqqqppppppppjjjjjjbbbbb eeeeeeeeehhhhhhhgggggnnnnnnqqqqqqqqqqqqqqppppppppjjjjjjbbbbb eeeeeeeeehhhhhhhgggggnnnnnnqqqqqqqqqqqqqqppppppppjjjjjjbbbbb eeeeeeeeehhhhhhhgggggnnnnnnqqqqqqqqqqqqqqppppppppjjjjjjbbbbb eeeeeeeeehhhhhhhgggggnnnnnnqqqqqqqqqqqqqqppppppppjjjjjjbbbbb eeeeeeeeehhhhhhhgggggnnnnnnqqqqqqqqqqqqqqppppppppjjjjjjbbbbb eeeeeeeeehhhhhhhgggggnnnnnnqqqqqqqqqqqqqqppppppppjjjjjjbbbbb eeeeeeeeehhhhhhhgggggnnnnnnqqqqqqqqqqqqqqppppppppjjjjjjbbbbb eeeeeeeeehhhhhhhgggggnnnnnnqqqqqqqqqqqqqqppppppppjjjjjjbbbbb eeeeeeeeehhhhhhhgggggnnnnnnkkkkkkkkkkkkkkkkkkkkkkjjjjjjbbbbb eeeeeeeeehhhhhhhgggggnnnnnnkkkkkkkkkkkkkkkkkkkkkkjjjjjjbbbbb eeeeeeeeehhhhhhhgggggnnnnnnkkkkkkkkkkkkkkkkkkkkkkjjjjjjbbbbb eeeeeeeeehhhhhhhgggggnnnnnnkkkkkkkkkkkkkkkkkkkkkkjjjjjjbbbbb dddddddddhhhhhhhgggggnnnnnnkkkkkkkkkkkkkkkkkkkkkkjjjjjjbbbbb dddddddddhhhhhhhgggggnnnnnnkkkkkkkkkkkkkkkkkkkkkkjjjjjjbbbbb dddddddddhhhhhhhgggggnnnnnnkkkkkkkkkkkkkkkkkkkkkkjjjjjjbbbbb dddddddddhhhhhhhgggggnnnnnnkkkkkkkkkkkkkkkkkkkkkkjjjjjjbbbbb dddddddddhhhhhhhgggggnnnnnnkkkkkkkkkkkkkkkkkkkkkkjjjjjjbbbbb dddddddddhhhhhhhgggggnnnnnnkkkkkkkkkkkkkkkkkkkkkkjjjjjjbbbbb dddddddddhhhhhhhgggggnnnnnnmmmmmmmmmmmmmmmmmmmmmcccccccccccc dddddddddiiiiiiiiiiiinnnnnnmmmmmmmmmmmmmmmmmmmmmcccccccccccc dddddddddiiiiiiiiiiiinnnnnnmmmmmmmmmmmmmmmmmmmmmcccccccccccc dddddddddiiiiiiiiiiiinnnnnnmmmmmmmmmmmmmmmmmmmmmcccccccccccc dddddddddiiiiiiiiiiiinnnnnnmmmmmmmmmmmmmmmmmmmmmcccccccccccc dddddddddiiiiiiiiiiiinnnnnnmmmmmmmmmmmmmmmmmmmmmcccccccccccc dddddddddiiiiiiiiiiiinnnnnnmmmmmmmmmmmmmmmmmmmmmcccccccccccc dddddddddiiiiiiiiiiiinnnnnnmmmmmmmmmmmmmmmmmmmmmcccccccccccc dddddddddiiiiiiiiiiiinnnnnnmmmmmmmmmmmmmmmmmmmmmcccccccccccc dddddddddiiiiiiiiiiiinnnnnnmmmmmmmmmmmmmmmmmmmmmcccccccccccc dddddddddiiiiiiiiiiiilllllllllllllllllllllllllllcccccccccccc dddddddddiiiiiiiiiiiilllllllllllllllllllllllllllcccccccccccc dddddddddiiiiiiiiiiiilllllllllllllllllllllllllllcccccccccccc dddddddddiiiiiiiiiiiilllllllllllllllllllllllllllcccccccccccc dddddddddiiiiiiiiiiiilllllllllllllllllllllllllllcccccccccccc dddddddddiiiiiiiiiiiilllllllllllllllllllllllllllcccccccccccc dddddddddiiiiiiiiiiiilllllllllllllllllllllllllllcccccccccccc dddddddddiiiiiiiiiiiilllllllllllllllllllllllllllcccccccccccc |
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2017-01-01, 13:42
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#36 |
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"Robert Gerbicz"
Oct 2005
Hungary
22·7·53 Posts |
For the modified puzzle (when different orientation of the rectangle is permitted) computed up to n=45, see the tilings at https://oeis.org/A279596/a279596.txt
One crazy tiling is for n=29, this is using 34 rectangles: Code:
a(29)=7 aaaaaaaaaaaaaaaaaaaaaaaaaaaeb dhhhhhhhhhhhhhhhhhhhhhhhhhheb dgkkkkkkkkkkkkkkkkkkkkkkkkkeb dgjnnnnnnnnnnnnnnnnnnnnnnnneb dgjmmooooooooooooooooooooooeb dgjmmiqBBBBBHHHHHHHHHHHHEEEeb dgjmmiqBBBBBHHHHHHHHHHHHEEEeb dgjmmiqBBBBBGGGGGGGGFFFFEEEeb dgjmmiqBBBBBGGGGGGGGFFFFEEEeb dgjmmiqBBBBBGGGGGGGGFFFFEEEeb dgjmmiqCCCCCCCCCCCCCFFFFEEEeb dgjmmiqCCCCCCCCCCCCCFFFFEEEeb dgjmmiqttDDDDDDDDDDDFFFFEEEeb dgjmmiqttDDDDDDDDDDDFFFFEEEeb dgjmmiqttvvzzzzzzzAAAAAAAAAeb dgjmmiqttvvzzzzzzzAAAAAAAAAeb dgjmmiqttvvzzzzzzzAAAAAAAAAeb dgjlliqttvvzzzzzzzwwwyyyyyyeb dgjlliqttvvuuuxxxxwwwyyyyyyeb dgjlliqttvvuuuxxxxwwwyyyyyyeb dgjlliqttvvuuuxxxxwwwyyyyyyeb dgjlliqttvvuuuxxxxwwwrrrrrrrb dgjlliqttvvuuuxxxxwwwrrrrrrrb dgjlliqttvvuuuxxxxwwwrrrrrrrb dgjlliqttvvuuussssssssssssssb dgjlliqttvvuuussssssssssssssb dgjlliqpppppppppppppppppppppb dgjllifffffffffffffffffffffff dcccccccccccccccccccccccccccc |
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2017-01-02, 18:05
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#37 |
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Nov 2016
24 Posts |
Very interesting solutions. This time, I already managed to find some of those optimal solutions already, but it's good to have all of them. Which one of those required the most time to find?
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2017-01-02, 19:34
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#38 | |
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"Robert Gerbicz"
Oct 2005
Hungary
22·7·53 Posts |
Quote:
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2017-01-04, 16:23
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#39 |
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Nov 2016
24 Posts |
If it would be easy, for values up to 24 or so (or whatever is easy), could you post solutions optimized for the most rectangles instead of the least rectangles?
For example, in the Variant for square 31, I have optimal solutions with 19 rectangles and 36 rectangles. Is that the full range? What other numbers of rectangles offer the optimal solution for square 31? I'd like to make a puzzle called the Mondrian Cube, where a square with many solutions has lengths on the four edges so that a cube can be folded. |
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2017-01-05, 09:06
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#40 | |
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"Robert Gerbicz"
Oct 2005
Hungary
27148 Posts |
Quote:
ps. Note that I've used a slightly different strategy: in the main search for fixed defect looking for tiling in descending order of the minimal rectangle's area from those rectangles that are in the square's corner. [The tiling is started with that rectangle with letter 'a', in the square's upper left corner]. See for example in the oeis sequence for n=5 the example used 7 rectangles, but there is also a tiling for 6 rectangles. Code:
a(3)=2; 3 rectangles; aab ccb ccb a(4)=2; 5 rectangles; aaab eedb eedb cccc a(5)=3; 6 rectangles; aaaab edddb efffb efffb ccccc a(5)=3; 7 rectangles; aaaab fggdb fggdb feeeb ccccc a(6)=3; 8 rectangles; aaaaab efdddb efhhhb efhhhb eggggb cccccc a(7)=3; 10 rectangles; aaaaabb djihhbb djihhbb djifffe djifffe djgggge dcccccc a(8)=3; 9 rectangles; aaaaaacb giieeecb giieeecb giifffcb giifffcb ghhfffcb ghhddddb ghhddddb a(9)=3; 11 rectangles; aaaaaaaab eeddddddb eeiijjjgb eeiijjjgb eeiijjjgb hhhkkkkgb hhhkkkkgb fffffffgb ccccccccc a(10)=4; 10 rectangles; aaaaaaaaab dddhhhhjjb dddhhhhjjb dddggiijjb eeeggiijjb eeeggiijjb eeeggiijjb eeeggffffb cccccffffb cccccffffb a(10)=4; 12 rectangles; aaaaaaaaab effddddddb effkkklljb effkkklljb effkkklljb ehhhhhlljb ehhhhhlljb eiiiiiiijb eggggggggb cccccccccc a(10)=4; 13 rectangles; aaaaaaaaab effddddddb effiijjjhb effiijjjhb effiikkkhb ellllkkkhb ellllkkkhb emmmmmmmhb eggggggggb cccccccccc a(10)=4; 14 rectangles; aaaaaacbbb fnmljjcbbb fnmljjcddd fnmljjcddd fnmljjcddd fnmliiiigg fnmliiiigg fnmkkkkkgg fnhhhhhhhh feeeeeeeee a(11)=4; 12 rectangles; aaaaaaaaaab eeddddddddb eekkkklllgb eekkkklllgb eekkkklllgb eejjjjlllgb eejjjjiiigb hhhhhhiiigb hhhhhhiiigb fffffffffgb ccccccccccc a(11)=4; 15 rectangles; aaaaaaaaaeb diiiiiiiieb dhllllllleb dhkoooonneb dhkoooonneb dhkjjmmnneb dhkjjmmgggb dhkjjmmgggb dhkjjmmgggb dhkjjffffff dcccccccccc a(12)=4; 14 rectangles; aaaaaaaaaaab effddddddddb effmmmmnnnjb effmmmmnnnjb effmmmmnnnjb effllllnnnjb effllllkkkjb ehhhhhhkkkjb ehhhhhhkkkjb eiiiiiiiiijb eggggggggggb cccccccccccc a(13)=4; 16 rectangles; aaaaaaaaaaaeb diiiiiimmmleb diiiiiimmmleb djjjjnnmmmleb djjjjnnpppleb djjjjnnpppleb dhhkknnpppleb dhhkknnpppleb dhhkkoooooleb dhhkkoooooleb dhhgggggggggb dhhffffffffff dcccccccccccc a(13)=4; 17 rectangles; aaaaaaaaaaghb emmmppppqqghb emmmppppqqghb emmmppppqqghb efnnnnnnqqghb efnnnnnnqqghb efjjllooooghb efjjllooooghb efjjllkkkkkhb efjjllkkkkkhb efjjiiiiiiiib efjjddddddddd efccccccccccc a(14)=4; 9 rectangles; aaaaaaaeeeffbb aaaaaaaeeeffbb aaaaaaaeeeffbb ddiiiiieeeffbb ddiiiiieeeffbb ddiiiiieeeffbb ddiiiiieeeffbb ddhhhhhhhhffbb ddhhhhhhhhffbb ddhhhhhhhhffbb ddggggggggggbb ddggggggggggbb ddcccccccccccc ddcccccccccccc a(15)=5; 17 rectangles; aaaaaaaaaaaaaab dfffffffffffffb diiiiiiiiiiiieb dnnnnnnnnnnnheb dmmqqqqqqpppheb dmmqqqqqqpppheb dmmlloooopppheb dmmlloooopppheb dmmlloooopppheb dmmllooookkkheb dmmlljjjjkkkheb dmmlljjjjkkkheb cccccjjjjkkkheb cccccgggggggheb cccccgggggggheb a(15)=5; 18 rectangles; aaaaaaaaaaaaaab eghfddddddddddb eghfmmmmmlllllb eghfmmmmmlllllb eghfmmmmmooonnb eghfqqrrrooonnb eghfqqrrrooonnb eghfqqrrrooonnb eghfqqrrrooonnb eghfqqppppppnnb eghfqqppppppnnb eghkkkkkkkkkkkb egjjjjjjjjjjjjb eiiiiiiiiiiiiib ccccccccccccccc a(15)=5; 19 rectangles; aaaaaaaaaaaaaeb djjjjjjjjjjjkeb drrrrrrrrrrmkeb dpppsssssssmkeb dpppsssssssmkeb dpppqqqqqnnmkeb dpppqqqqqnnmkeb dhhiioooonnmkeb dhhiioooonnmkeb dhhiioooonnmkeb dhhiillllllmkeb dhhiillllllmkeb dhhiigggggggggb dhhffffffffffff dcccccccccccccc a(16)=5; 19 rectangles; aaaaaaaaaaaaaaab efffdddddddddddb efffhhhhhhhhjigb efffhhhhhhhhjigb efffmmrrrrrrjigb ennnmmrrrrrrjigb ennnmmssssqqjigb ennnmmssssqqjigb ennnmmssssqqjigb ennnmmssssqqjigb eoooopppppqqjigb eoooopppppqqjigb eoooopppppqqjigb elllllllllllligb ekkkkkkkkkkkkkgb cccccccccccccccc a(16)=5; 20 rectangles; aaaaaaaaaaaabbbb dfhigeeeeeeebbbb dfhigeeeeeeebbbb dfhignnnnnooooom dfhignnnnnooooom dfhigrrqqqooooom dfhigrrqqqsssppm dfhigrrqqqsssppm dfhigrrqqqsssppm dfhigrrqqqsssppm dfhigrrttttttppm dfhigrrttttttppm dfhilllllllllllm dfhkkkkkkkkkkkkk dfjjjjjjjjjjjjjj dccccccccccccccc a(17)=5; 7 rectangles; aaaaaaaaaaaaabbbb aaaaaaaaaaaaabbbb aaaaaaaaaaaaabbbb dddffffggggggbbbb dddffffggggggbbbb dddffffggggggbbbb dddffffggggggbbbb dddffffggggggbbbb dddffffggggggbbbb dddffffggggggbbbb dddffffeeeeeeeeee dddffffeeeeeeeeee dddffffeeeeeeeeee dddffffeeeeeeeeee dddcccccccccccccc dddcccccccccccccc dddcccccccccccccc a(17)=5; 21 rectangles; aaaaaaaaaaaaaaaeb djjjjjjjjjjjjjjeb dinnnnnnnnnnnnneb dimmkoqqqqrrrrreb dimmkoqqqqrrrrreb dimmkoqqqqrrrrreb dimmkopptttuuuueb dimmkopptttuuuueb dimmkopptttuuuueb dimmkopptttuuuueb dillkoppssssssseb dillkoppssssssseb dillkopphhhhhhhhb dillkopphhhhhhhhb dillkgggggggggggb dillkffffffffffff dcccccccccccccccc a(18)=6; 12 rectangles; aaaaaaaaaccbbbbbbb aaaaaaaaaccbbbbbbb aaaaaaaaaccbbbbbbb hhllllkkkccbbbbbbb hhllllkkkcceeeffdd hhllllkkkcceeeffdd hhllllkkkcceeeffdd hhllllkkkcceeeffdd hhllllkkkcceeeffdd hhllllkkkcceeeffdd hhjjjjkkkcceeeffdd hhjjjjkkkcceeeffdd hhjjjjkkkcceeeffdd hhjjjjiiiiiiiiffdd hhjjjjiiiiiiiiffdd hhjjjjiiiiiiiiffdd hhggggggggggggggdd hhggggggggggggggdd a(18)=6; 15 rectangles; aaaaaaaaaabbbbbbbb aaaaaaaaaabbbbbbbb nnnmmooeeebbbbbbbb nnnmmooeeejjjjggff nnnmmooeeejjjjggff nnnmmooeeejjjjggff nnnmmooeeejjjjggff nnnmmooeeejjjjggff nnnmmooeeejjjjggff nnnmmookkkkkkkggff lllmmookkkkkkkggff lllmmookkkkkkkggff lllmmhhhhhhhhhhhff lllmmhhhhhhhhhhhff llliiiiiiiiicccccc llliiiiiiiiicccccc ddddddddddddcccccc ddddddddddddcccccc a(18)=6; 18 rectangles; aaaaaaaaaaaaaaaaab eddddddddddddddddb eqqqppppppppppgggb eqqqppppppppppgggb eqqqrrrrrroooogggb eqqqrrrrrroooogggb eqqqrrrrrroooogggb eiinnnnnnnoooogggb eiinnnnnnnmmmmmffb eiinnnnnnnmmmmmffb eiijjjllllmmmmmffb eiijjjllllmmmmmffb eiijjjllllkkkkkffb eiijjjllllkkkkkffb eiijjjllllkkkkkffb eiijjjhhhhhhhhhffb eiijjjhhhhhhhhhffb cccccccccccccccccc a(18)=6; 19 rectangles; aaaaaaaaaaaaaaaaab eggddddddddddddddb eggmmmmmmmmmsssrrb eggmmmmmmmmmsssrrb eggnnnppppppsssrrb eggnnnppppppsssrrb eggnnnppppppsssrrb eggnnnoooooqqqqrrb eggnnnoooooqqqqrrb eggnnnoooooqqqqrrb eiiiiiiiiiiqqqqrrb eiiiiiiiiiiqqqqrrb ejjjjjjjjjjjjjjjjb ehhhhhhhlllllkkkkb ehhhhhhhlllllkkkkb fffffffflllllkkkkb fffffffflllllkkkkb cccccccccccccccccc a(18)=6; 20 rectangles; aaaaaaaaaaaaaaaaab egfddddddddddddddb egfkkkkklljjjjjjjb egfkkkkklljjjjjjjb egfkkkkkllttttsssb egfnnmmmllttttsssb egfnnmmmllttttsssb egfnnmmmllttttsssb egfnnmmmllttttsssb egfnnmmmqqqqqqqqqb egfnnmmmqqqqqqqqqb egfnnpppppppprrrrb egfnnpppppppprrrrb egfoooooooooorrrrb egfoooooooooorrrrb egiiiiiiiiiiiiiiib ehhhhhhhhhhhhhhhhb cccccccccccccccccc a(18)=6; 21 rectangles; aaaaaaaaaaaaaaaaab ejjjjddddddddddddb ejjjjmmmmmmmoonngb ejjjjmmmmmmmoonngb elllllqqqqqqoonngb elllllqqqqqqoonngb elllllqqqqqqoonngb ekkrrrrrrrrroonngb ekkrrrrrrrrroonngb ekktttppppppppnngb ekktttppppppppnngb ekktttuuuusssiiigb ekktttuuuusssiiigb ekktttuuuusssiiigb ekktttuuuusssiiigb hhhhhhhhhhhhhiiigb ffffffffffffffffgb cccccccccccccccccc a(18)=6; 22 rectangles; aaaaaaaaaaaaaaaaaa kkkkkkkkkkkkkkkkml qqqqqqqqqqqqqqrrml ppppppppppppssrrml ffffffffdottssrrml ffffffffdottssrrml eeeeegggdottssrrml eeeeegggdottssrrml eeeeegggdottssrrml cchhhgggdottvvvvml cchhhjjjdottvvvvml cchhhjjjdottvvvvml cchhhjjjdouuuuuuml cchhhjjjdouuuuuuml cchhhjjjdonnnnnnnl cciiiiiidonnnnnnnl cciiiiiidbbbbbbbbb cciiiiiidbbbbbbbbb a(18)=6; 23 rectangles; aaaaaaaaaaaaaaaaeb dhhhhhhhhhhhhhhheb dgkkkkkkmmmmmmmmeb dgkkkkkkmmmmmmmmeb dgjllllllllllllleb dgjippppppppppppeb dgjiqqqqqqqttssseb dgjiqqqqqqqttssseb dgjioovvwwwttssseb dgjioovvwwwttssseb dgjioovvwwwttssseb dgjioovvwwwttrrrrb dgjioovvuuuuurrrrb dgjioovvuuuuurrrrb dgjioovvuuuuurrrrb dgjioonnnnnnnnnnnb dgjiffffffffffffff dccccccccccccccccc a(18)=6; 24 rectangles; aaaaaaaaaaaaaaaaeb jjjjjjjjjjjjjjjkeb mmmmmmmmmmmmmmnkeb lllllllllllllonkeb iiqqqqqqqqqqqonkeb iippppppwwwwwonkeb iippppppwwwwwonkeb iihsstttwwwwwonkeb iihsstttxxxvvonkeb iihsstttxxxvvonkeb ddhsstttxxxvvonkeb ddhsstttxxxvvonkeb ddhrrrruuuuvvonkeb ddhrrrruuuuvvonkeb ddhrrrruuuuvvonkeb ddhrrrrffffffffffb ddhgggggggcccccccc ddhgggggggcccccccc a(18)=6; 25 rectangles; aaaaaaaaaaaaaaaghb eeeeeeeeeeuuuuughb dppposssssuuuuughb dppposssssuuuuughb dppporyyyyyyyvvghb dppporyyyyyyyvvghb dfqqorxxxxwwwvvghb dfqqorxxxxwwwvvghb dfqqorxxxxwwwvvghb dfqqorxxxxwwwvvghb dfqqorttttwwwvvghb dfqqorttttmmmmmmhb dfnnorttttmmmmmmhb dfnnorlllllllllllb dfnnokkkkkkkkkkkkb dfnnoiiiiiiiiiiiii dfnnjjjjjjjjjjjjjj dfcccccccccccccccc a(19)=6; 11 rectangles; aaaaaaaaaaaaaaaabbb aaaaaaaaaaaaaaaabbb ddfffeeeeeeeeeeebbb ddfffeeeeeeeeeeebbb ddfffeeeeeeeeeeebbb ddfffkkkkkkhhhhhbbb ddfffkkkkkkhhhhhbbb ddfffkkkkkkhhhhhbbb ddfffkkkkkkhhhhhbbb ddfffkkkkkkhhhhhbbb ddfffkkkkkkhhhhhbbb ddfffjjjjjjjjjjcccc ddfffjjjjjjjjjjcccc ddfffjjjjjjjjjjcccc ddggggggiiiiiiicccc ddggggggiiiiiiicccc ddggggggiiiiiiicccc ddggggggiiiiiiicccc ddggggggiiiiiiicccc a(19)=6; 17 rectangles; aaaaaaaaaaaaaaaaaaa dddddddddhhhhhhhhhh dddddddddhhhhhhhhhh eeeeemmmmmmmmjjjjjj eeeeemmmmmmmmjjjjjj eeeeemmmmmmmmjjjjjj eeeeennnnnnnnnnnnii ccgggnnnnnnnnnnnnii ccggglllkkqqqqqqqii ccggglllkkqqqqqqqii ccggglllkkqqqqqqqii ccggglllkkppppoooii ccggglllkkppppoooii ccggglllkkppppoooii ccggglllkkppppoooii ccffffffkkppppoooii ccffffffkkppppoooii ccffffffbbbbbbbbbbb ccffffffbbbbbbbbbbb a(19)=6; 20 rectangles; aaaaaaaaaaaaaaaaaab efddddddddddddddddb efmmnnnkkkkkkkkkhhb efmmnnnkkkkkkkkkhhb efmmnnnoooolllllhhb efmmnnnoooolllllhhb efmmnnnoooolllllhhb efmmnnnoooolllllhhb efmmnnnoooojjjjjhhb efmmpppppppjjjjjhhb efmmpppppppjjjjjhhb efmmpppppppqqqqiiib efsssttttttqqqqiiib efsssttttttqqqqiiib efsssttttttqqqqiiib efsssrrrrrrrrrriiib efsssrrrrrrrrrriiib egggggggggggggggggb ccccccccccccccccccc a(19)=6; 21 rectangles; aaaaaaaaaaaaaaaaaab egffddddddddddddddb egffjjjsssssssssslb egffjjjsssssssssslb egffjjjrrqqttttttlb egffjjjrrqqttttttlb egffjjjrrqqttttttlb egffjjjrrqquuuuoolb egiiiiirrqquuuuoolb egiiiiirrqquuuuoolb egiiiiirrqquuuuoolb egiiiiirrqquuuuoolb egmmmmmmmqqppppoolb egmmmmmmmqqppppoolb egnnnnnnnnnppppoolb egnnnnnnnnnppppoolb egkkkkkkkkkkkkkkklb ehhhhhhhhhhhhhhhhhb ccccccccccccccccccc a(19)=6; 22 rectangles; aaaaaaaaaaaaaaaaaab eghfddddddddddddddb eghfmmmmmnnlllllllb eghfmmmmmnnlllllllb eghfmmmmmnnvvvvuuub eghfppooonnvvvvuuub eghfppooonnvvvvuuub eghfppooonnvvvvuuub eghfppooonnvvvvuuub eghfppooosssssssssb eghfppooosssssssssb eghfpprrrrrrrrttttb eghfpprrrrrrrrttttb eghfqqqqqqqqqqttttb eghfqqqqqqqqqqttttb eghkkkkkkkkkkkkkkkb egjjjjjjjjjjjjjjjjb eiiiiiiiiiiiiiiiiib ccccccccccccccccccc a(19)=6; 23 rectangles; aaaaaaaaaaaaaaaaaeb djjjjjjjjjjjjjjjjeb dinnnnnnnnnnnnnnneb dilooooooooooooooeb dilmuuuttttttttrreb dilmuuuttttttttrreb dilmuuuwwwwwwssrreb dilmuuuwwwwwwssrreb dilmuuuwwwwwwssrreb dilmkkvvvvvvvssrreb dilmkkvvvvvvvssrreb dilmkkpppqqqqssrreb dilmkkpppqqqqhhhhhb dilmkkpppqqqqhhhhhb dilmkkpppqqqqhhhhhb dilmkkpppgggggggggb dilmkkpppgggggggggb dilmkkfffffffffffff dcccccccccccccccccc a(19)=6; 24 rectangles; aaaaaaaaaaaaaaaaaeb djjjjjjjoooooooooeb djjjjjjjoooooooooeb dinnnnnnnnnnnnnnneb dilppppppppppppppeb dilmuuuuuuuuuuuuueb dilmxxvvvvvvssttteb dilmxxvvvvvvssttteb dilmxxvvvvvvssttteb dilmxxwwwwrrssttteb dilmxxwwwwrrssttteb dilmxxwwwwrrssttteb dilmxxwwwwrrsshhhhb dilmkkkqqqrrsshhhhb dilmkkkqqqrrsshhhhb dilmkkkqqqrrggggggb dilmkkkqqqrrggggggb dilmkkkffffffffffff dcccccccccccccccccc a(20)=4; 8 rectangles; aaaaaaaaaaaaaaaabbbb aaaaaaaaaaaaaaaabbbb aaaaaaaaaaaaaaaabbbb dddgggggggggggggbbbb dddgggggggggggggbbbb dddgggggggggggggbbbb dddgggggggggggggbbbb dddfffffhhhhhhhhbbbb dddfffffhhhhhhhhbbbb dddfffffhhhhhhhhbbbb dddfffffhhhhhhhhbbbb dddfffffhhhhhhhhbbbb dddfffffhhhhhhhhbbbb dddfffffeeeeeeeeeeee dddfffffeeeeeeeeeeee dddfffffeeeeeeeeeeee dddfffffeeeeeeeeeeee dddccccccccccccccccc dddccccccccccccccccc dddccccccccccccccccc a(21)=6; 13 rectangles; aaaaaaaaaaaaaaaabbbbb aaaaaaaaaaaaaaaabbbbb eeeffffffiiiiiiibbbbb eeeffffffiiiiiiibbbbb eeeffffffiiiiiiibbbbb eeeffffffiiiiiiibbbbb eeeffffffiiiiiiibbbbb eeehhhhhhhhhhhhhhhhhh eeehhhhhhhhhhhhhhhhhh eeeggggggggggggjjjjjj eeeggggggggggggjjjjjj eeeggggggggggggjjjjjj ddddmmmmmmmmmmmjjjjjj ddddmmmmmmmmmmmjjjjjj ddddmmmmmmmmmmmjjjjjj ddddlllllllllkkkkkkkk ddddlllllllllkkkkkkkk ddddlllllllllkkkkkkkk ddddlllllllllkkkkkkkk ddddccccccccccccccccc ddddccccccccccccccccc a(21)=6; 16 rectangles; aaaaaaaaaaaaaabbbbbbb aaaaaaaaaaaaaabbbbbbb eeffffffffffffbbbbbbb eeffffffffffffbbbbbbb eehhhhhhhhhhhhhjjjjii eehhhhhhhhhhhhhjjjjii eegggmmmmnnnnnnjjjjii eegggmmmmnnnnnnjjjjii eegggmmmmnnnnnnjjjjii eegggmmmmnnnnnnjjjjii eegggmmmmppppppppppii eegggmmmmppppppppppii eegggmmmmppppppppppii eegggkkkkkkkkkoooooii eegggkkkkkkkkkoooooii eegggkkkkkkkkkoooooii ddddddlllllllloooooii ddddddlllllllloooooii ddddddlllllllloooooii ddddddccccccccccccccc ddddddccccccccccccccc a(21)=6; 21 rectangles; aaaaaaaaaaaaaaaaaaaaa ggggggggggggggggggggh iiiiiioooooooooooopph iiiiiioooooooooooopph iiiiiinnnnnnnnnnrrpph iiiiiinnnnnnnnnnrrpph ffjjjkkkuuuuuuuurrpph ffjjjkkkuuuuuuuurrpph ffjjjkkkuuuuuuuurrpph ffjjjkkkttttttssrrpph ffjjjkkkttttttssrrpph ffjjjkkkttttttssrrpph ffjjjlllllllllssrrpph ffjjjlllllllllssqqqqh ffeeeeedddmmmmssqqqqh ffeeeeedddmmmmssqqqqh ffeeeeedddmmmmssqqqqh ffeeeeedddmmmmssqqqqh cccccccdddmmmmssqqqqh cccccccdddbbbbbbbbbbb cccccccdddbbbbbbbbbbb a(21)=6; 24 rectangles; aaaaaaaaaaaaaaaaaaaab eghfddddddddddddddddb eghfqqrrrooooooooollb eghfqqrrrooooooooollb eghfqqrrrsssspppppllb eghfqqrrrsssspppppllb eghfqqrrrsssspppppllb eghfqqrrrsssspppppllb eghfqqrrrssssnnnnnllb eghfqqtttttttnnnnnllb eghfqqtttttttnnnnnllb eghfqqtttttttuuuummmb eghfwwwxxxxxxuuuummmb eghfwwwxxxxxxuuuummmb eghfwwwxxxxxxuuuummmb eghfwwwvvvvvvvvvvmmmb eghfwwwvvvvvvvvvvmmmb eghkkkkkkkkkkkkkkkkkb egjjjjjjjjjjjjjjjjjjb eiiiiiiiiiiiiiiiiiiib ccccccccccccccccccccc a(21)=6; 25 rectangles; aaaaaaaaaaaaaaaaaafhb eeeeeeeeeeeeeeeeegfhb dmmooooooooxxxyyrgfhb dmmooooooooxxxyyrgfhb dmmnnvvvvvvxxxyyrgfhb dmmnnvvvvvvxxxyyrgfhb dmmnnvvvvvvxxxyyrgfhb dmmnnuuuuwwwwwyyrgfhb dmmnnuuuuwwwwwyyrgfhb dmmnnuuuuwwwwwyyrgfhb dmmnnuuuuwwwwwyyrgfhb dmmnnuuuuttttsssrgfhb dlllqqqqqttttsssrgfhb dlllqqqqqttttsssrgfhb dlllqqqqqttttsssrgfhb dlllpppppppppsssrgfhb dlllpppppppppsssrgfhb dlllkkkkkkkkkkkkkkkhb dllljjjjjjjjjjjjjjjjb diiiiiiiiiiiiiiiiiiib dcccccccccccccccccccc a(21)=6; 26 rectangles; aaaaaaaaaaaaaaaaaaabb diiiiiiiiiiiiiiiiiibb dvvvvvvvvvvvvvvvvvhbb dzxxxxxxxxxxxxxxxxhbb dzywwwwwwwwwwwwwwwhbb dzytuuuuuuuuuuuuuuhbb dzytqqqqqrrrrrrrrrhbb dzytqqqqqrrrrrrrrrhbb dzytqqqqqlllllkkkkhbb dzytqqqqqlllllkkkkhbb dzytssppplllllkkkkhee dzytsspppoooggkkkkhee dzytsspppoooggkkkkhee dzytsspppoooggjjjjhee dzytsspppoooggjjjjhee dzytsspppoooggjjjjhee dzytssmmmmmmggjjjjhee dzytssmmmmmmggfffffff dzytssmmmmmmggfffffff dzynnnnnnnncccccccccc dzynnnnnnnncccccccccc a(22)=6; 13 rectangles; aaaaaaaaaaaaaaaaabbbbb aaaaaaaaaaaaaaaaabbbbb ggffffffffeeeeeeebbbbb ggffffffffeeeeeeebbbbb ggffffffffeeeeeeebbbbb ggffffffffeeeeeeebbbbb ggffffffffeeeeeeebbbbb ggjjjiiiiddddddddddddd ggjjjiiiiddddddddddddd ggjjjiiiiddddddddddddd ggjjjiiiimmmmmmllllccc ggjjjiiiimmmmmmllllccc ggjjjiiiimmmmmmllllccc ggjjjiiiimmmmmmllllccc ggjjjiiiimmmmmmllllccc ggjjjiiiimmmmmmllllccc ggjjjkkkkkkkkkkllllccc ggjjjkkkkkkkkkkllllccc ggjjjkkkkkkkkkkllllccc ggjjjkkkkkkkkkkllllccc hhhhhhhhhhhhhhhhhhhccc hhhhhhhhhhhhhhhhhhhccc a(22)=6; 18 rectangles; aaaaaaaaaaaabbbbbbbbbb aaaaaaaaaaaabbbbbbbbbb ddddeeccccccbbbbbbbbbb ddddeeccccccnnnnnnnnll ddddeeccccccnnnnnnnnll ddddeeccccccnnnnnnnnll ddddeeooooooooooooooll ddddeeooooooooooooooll ggffeerrrrrrqqqqqmmmll ggffeerrrrrrqqqqqmmmll ggffeerrrrrrqqqqqmmmll ggffeerrrrrrqqqqqmmmll ggffeerrrrrrqqqqqmmmll ggffeepppppppkkkkmmmll ggffeepppppppkkkkmmmll ggffeepppppppkkkkmmmll ggffeepppppppkkkkjjjjj ggffiiiiiiiiikkkkjjjjj ggffiiiiiiiiikkkkjjjjj ggffiiiiiiiiikkkkjjjjj gghhhhhhhhhhhhhhhjjjjj gghhhhhhhhhhhhhhhjjjjj a(22)=6; 23 rectangles; aaaaaaaaaaaaaaaaaaaaab efdddddddddddddddddddb efmmmmmmmmmmjjjjjjjjjb efmmmmmmmmmmjjjjjjjjjb efpppppppplllllllllllb efpppppppplllllllllllb efppppppppvvvvuukkkkkb efoorrrrrrvvvvuukkkkkb efoorrrrrrvvvvuukkkkkb efoorrrrrrvvvvuukkkkkb efoorrrrrrvvvvuutttiib efooqqqssswwwwuutttiib efooqqqssswwwwuutttiib efooqqqssswwwwuutttiib efooqqqssswwwwuutttiib efooqqqssswwwwuutttiib efooqqqssswwwwuutttiib efooqqqnnnnnnnnnnnniib efooqqqnnnnnnnnnnnniib ehhhhhhhhhhhhhhhhhhiib eggggggggggggggggggggb cccccccccccccccccccccc a(22)=6; 27 rectangles; aaaaaaaaaaaaaaaaaaaadb ellllllllllllllllllldb emmmmmppppppqqqqqqqrdb emmmmmppppppqqqqqqqrdb emmmmmppppppqqqqqqqrdb einnnnnnnnnnnnnnnnnrdb eiooooooooooooooossrdb eijuuuuuxxxAAAAyyssrdb eijuuuuuxxxAAAAyyssrdb eijuuuuuxxxAAAAyyssrdb eijuuuuuxxxAAAAyyssrdb eijkkvvvxxxAAAAyyssrdb eijkkvvvxxxzzzzyyssrdb eijkkvvvwwwzzzzyyssrdb eijkkvvvwwwzzzzyyssrdb eijkkvvvwwwzzzzyyssrdb eijkkvvvwwwttttttttrdb eijkkvvvwwwttttttttrdb eijkkhhhhhhhhhhhhhhhhb eijffffffffffffffffffb eijgggggggggcccccccccc eijgggggggggcccccccccc a(23)=6; 16 rectangles; aaaaaaaaaaaaaaaaaeeeebb aaaaaaaaaaaaaaaaaeeeebb ppookkkkkkkiiiiiieeeebb ppookkkkkkkiiiiiieeeebb ppookkkkkkkiiiiiieeeebb ppookkkkkkkiiiiiieeeebb ppookkkkkkkiiiiiieeeebb ppoollljjjjjjjjffeeeebb ppoollljjjjjjjjffggggbb ppoollljjjjjjjjffggggbb ppoollljjjjjjjjffggggbb ppoolllmmmmmhhhffggggbb ppoolllmmmmmhhhffggggbb ppoolllmmmmmhhhffggggbb ppoolllmmmmmhhhffggggbb ppoolllmmmmmhhhffggggbb ppoolllmmmmmhhhffggggbb ppnnnnnnnnnnhhhffcccccc ppnnnnnnnnnnhhhffcccccc ppnnnnnnnnnnhhhffcccccc ddddddddddddhhhffcccccc ddddddddddddhhhffcccccc ddddddddddddhhhffcccccc a(23)=6; 25 rectangles; aaaaaaaaaaaaaaaaaaaaaab eeeeeeeeeeeeeeeeeeggfdb nnoooommmmmmmmmmmmggfdb nnoooommmmmmmmmmmmggfdb nnooootttttxxyyyvvggfdb nnooootttttxxyyyvvggfdb nnooootttttxxyyyvvggfdb nnooootttttxxyyyvvggfdb nnssssssuuuxxyyyvvggfdb nnssssssuuuxxyyyvvggfdb nnssssssuuuxxyyyvvggfdb nnssssssuuuxxyyyvvggfdb qqqqqqqquuuxxwwwvvggfdb qqqqqqqquuuxxwwwllllfdb qqqqqqqquuuxxwwwllllfdb pppppprrrrrrrwwwllllfdb pppppprrrrrrrwwwllllfdb pppppprrrrrrrwwwllllfdb jjjjjjjjjjjjjjjjjjjjfdb kkkkkkkkkkkiiiiiiiiiidb kkkkkkkkkkkiiiiiiiiiidb hhhhhhhhhhhhhhhhhhhhhdb ccccccccccccccccccccccc a(24)=6; 10 rectangles; aaaaaaaaaaaaaaddddddbbbb aaaaaaaaaaaaaaddddddbbbb aaaaaaaaaaaaaaddddddbbbb aaaaaaaaaaaaaaddddddbbbb gggfffffffffffddddddbbbb gggfffffffffffddddddbbbb gggfffffffffffddddddbbbb gggfffffffffffddddddbbbb gggfffffffffffddddddbbbb gggjjjjjeeeeeeeeeeeebbbb gggjjjjjeeeeeeeeeeeebbbb gggjjjjjeeeeeeeeeeeebbbb gggjjjjjeeeeeeeeeeeebbbb gggjjjjjeeeeeeeeeeeebbbb gggjjjjjiiiiiiiiiicccccc gggjjjjjiiiiiiiiiicccccc gggjjjjjiiiiiiiiiicccccc gggjjjjjiiiiiiiiiicccccc gggjjjjjiiiiiiiiiicccccc gggjjjjjiiiiiiiiiicccccc ggghhhhhhhhhhhhhhhcccccc ggghhhhhhhhhhhhhhhcccccc ggghhhhhhhhhhhhhhhcccccc ggghhhhhhhhhhhhhhhcccccc a(24)=6; 27 rectangles; aaaaaaaaaaaaaaaaaaaaaaab fjjjjjjjjjjjjjjjjjjjjjdb fkkkkkkkkkkkkkkkkkkkkmdb fhlllllllllllllllllllmdb fhipppssssuuuuuuuuuvvmdb fhipppssssuuuuuuuuuvvmdb fhipppsssstttttttwwvvmdb fhipppsssstttttttwwvvmdb fhipppsssstttttttwwvvmdb fhippprrrrrrrrAAAwwvvmdb fhippprrrrrrrrAAAwwvvmdb fhippprrrrrrrrAAAwwvvmdb fhiggqqqqxxxxxAAAwwvvmdb fhiggqqqqxxxxxAAAwwvvmdb fhiggqqqqxxxxxAAAwwvvmdb fhiggqqqqxxxxxAAAwwvvmdb fhiggqqqqzzzzzzzzzzzzmdb fhiggqqqqzzzzzzzzzzzzmdb fhiggooooooyyyyyyyyyymdb fhiggooooooyyyyyyyyyymdb fhiggoooooonnnnnnnnnnndb fhiggoooooonnnnnnnnnnndb fhiggeeeeeeeeeeeeeeeeeeb cccccccccccccccccccccccc a(25)=6; 14 rectangles; aaaaaaaaaaaaaaeeeeeefffbb aaaaaaaaaaaaaaeeeeeefffbb aaaaaaaaaaaaaaeeeeeefffbb ddhhhgggggggggeeeeeefffbb ddhhhgggggggggeeeeeefffbb ddhhhgggggggggeeeeeefffbb ddhhhgggggggggeeeeeefffbb ddhhhgggggggggeeeeeefffbb ddhhhmmmmmmmmlllllllfffbb ddhhhmmmmmmmmlllllllfffbb ddhhhmmmmmmmmlllllllfffbb ddhhhmmmmmmmmlllllllfffbb ddhhhmmmmmmmmlllllllfffbb ddhhhmmmmmmmmlllllllfffbb ddhhhnnnnnnnnnnnnkkkkkkbb ddhhhnnnnnnnnnnnnkkkkkkbb ddhhhnnnnnnnnnnnnkkkkkkbb ddhhhnnnnnnnnnnnnkkkkkkbb ddjjjjjjjjjjjjjjjkkkkkkbb ddjjjjjjjjjjjjjjjkkkkkkbb ddjjjjjjjjjjjjjjjkkkkkkbb ddiiiiiiiiiiiiiiiiiiiiibb ddiiiiiiiiiiiiiiiiiiiiibb ddccccccccccccccccccccccc ddccccccccccccccccccccccc a(26)=6; 15 rectangles; aaaaaaaaaaaaaaaaaaaaaabbbb aaaaaaaaaaaaaaaaaaaaaabbbb ddgggggggggggggghhhhhhbbbb ddgggggggggggggghhhhhhbbbb ddgggggggggggggghhhhhhbbbb ddfflllkkkkkkkkkhhhhhhbbbb ddfflllkkkkkkkkkhhhhhhbbbb ddfflllkkkkkkkkkhhhhhhbbbb ddfflllkkkkkkkkkhhhhhhbbbb ddfflllkkkkkkkkkhhhhhhbbbb ddffllliiiiiiiiiiiiiiibbbb ddffllliiiiiiiiiiiiiiijjjj ddffllliiiiiiiiiiiiiiijjjj ddffllloooooooonnnnnnnjjjj ddffllloooooooonnnnnnnjjjj ddffllloooooooonnnnnnnjjjj ddffllloooooooonnnnnnnjjjj ddffllloooooooonnnnnnnjjjj ddffllloooooooonnnnnnnjjjj ddffeeeeeemmmmmmmmmmmmjjjj ddffeeeeeemmmmmmmmmmmmjjjj ddffeeeeeemmmmmmmmmmmmjjjj ddffeeeeeemmmmmmmmmmmmjjjj ddffeeeeeecccccccccccccccc ddffeeeeeecccccccccccccccc ddffeeeeeecccccccccccccccc a(26)=6; 32 rectangles; aaaaaaaaaaaaaaaaaaaaaaaggb eeeeeeeeeeeeeeeeeeetttoggb djjjjjjjjjjjjuuuuuutttoggb djjjjjjjjjjjjuuuuuutttoggb dfknnnnnnnnnnuuuuuutttoggb dfknnnnnnnnnnvvvvwwtttoggb dfklmyyyzzzzzvvvvwwtttoggb dfklmyyyzzzzzvvvvwwtttoggb dfklmyyyzzzzzvvvvwwxxxoggb dfklmyyyzzzzzvvvvwwxxxoppb dfklmyyyFFFFFFFFFwwxxxoppb dfklmyyyFFFFFFFFFwwxxxoppb dfklmssDDDDEEEEEEwwxxxoppb dfklmssDDDDEEEEEEwwxxxoppb dfklmssDDDDEEEEEEwwxxxoppb dfklmssDDDDEEEEEEwwxxxoppb dfklmssDDDDBBBBBBBBBBBoppb dfklmssDDDDBBBBBBBBBBBoppb dfklmssCCCCCCCCAAAAAAAoppb dfklmssCCCCCCCCAAAAAAAoppb dfklmssCCCCCCCCAAAAAAAoppb dfklmssrrrrrrrrrrrrrrrrrrb dfklmqqqqqqqqqqqqqqqqqqqqb dfklmhhhhhhhhhhhhhhhhhhhhh dfkliiiiiiiiiiiiiiiiiiiiii dfcccccccccccccccccccccccc a(27)=7; 19 rectangles; aaaaaaaaaaaaaaaaaaabbbbbbbb aaaaaaaaaaaaaaaaaaabbbbbbbb gghhhhheeeeeeeeeeeebbbbbbbb gghhhhheeeeeeeeeeeebbbbbbbb gghhhhheeeeeeeeeeeebbbbbbbb gghhhhhdddddddddddddddddddd gghhhhhdddddddddddddddddddd gghhhhhiiiiiiiiiiiiiiiiiicc gghhhhhiiiiiiiiiiiiiiiiiicc ggooooooooooooooooooooojjcc ggooooooooooooooooooooojjcc ggnnnpppppppppssssssqqqjjcc ggnnnpppppppppssssssqqqjjcc ggnnnpppppppppssssssqqqjjcc ggnnnpppppppppssssssqqqjjcc ggnnnmmmmmllllssssssqqqjjcc ggnnnmmmmmllllssssssqqqjjcc ggnnnmmmmmllllssssssqqqjjcc ggnnnmmmmmllllrrrrrrqqqjjcc ggnnnmmmmmllllrrrrrrqqqjjcc ggnnnmmmmmllllrrrrrrqqqjjcc ggnnnmmmmmllllrrrrrrqqqjjcc ggnnnmmmmmllllrrrrrrqqqjjcc ffffffffffllllrrrrrrqqqjjcc ffffffffffkkkkkkkkkkkkkjjcc ffffffffffkkkkkkkkkkkkkjjcc ffffffffffkkkkkkkkkkkkkjjcc a(27)=7; 30 rectangles; aaaaaaaaaaaaaaaaaaaaaaaaaab egjifdddddddddddddddddddddb egjifooooooooppnnnnnnnnnnnb egjifooooooooppnnnnnnnnnnnb egjifooooooooppAAzzzzzzzzzb egjifrrrrrrqqppAAzzzzzzzzzb egjifrrrrrrqqppAAzzzzzzzzzb egjifrrrrrrqqppAADDDDDDDyyb egjifrrrrrrqqppAADDDDDDDyyb egjiftttsssqqppAADDDDDDDyyb egjiftttsssqqppAACCCCBBByyb egjiftttsssqqppAACCCCBBByyb egjiftttsssqqppAACCCCBBByyb egjiftttsssqqppAACCCCBBByyb egjiftttsssqqppAACCCCBBByyb egjiftttsssqqppAACCCCBBByyb egjiftttvvvvvvvvvvvvvBBByyb egjiftttvvvvvvvvvvvvvBBByyb egjifuuuuuuuxxxxxxxxxxxxyyb egjifuuuuuuuxxxxxxxxxxxxyyb egjifuuuuuuuwwwwwwwwwwwwwwb egjifuuuuuuuwwwwwwwwwwwwwwb egjimmmmmmmmmmmmmmmmmmmmmmb egjlllllllllllllllllllllllb egkkkkkkkkkkkkkkkkkkkkkkkkb ehhhhhhhhhhhhhhhhhhhhhhhhhb ccccccccccccccccccccccccccc a(27)=7; 31 rectangles; aaaaaaaaaaaaaaaaaaaaaaaaaab egfdddddddddddddddddddddddb egfklljjjjjjjjjjjjjjjjjjjjb egfkllqqyyyyyyyyyyyCCCCAApb egfkllqqyyyyyyyyyyyCCCCAApb egfkllqqxxxDDDDDDDDCCCCAApb egfkllqqxxxDDDDDDDDCCCCAApb egfkllqqxxxDDDDDDDDCCCCAApb egfkllqqxxxEEEEEEEEEEEEAApb egfkllqqxxxEEEEEEEEEEEEAApb egfkllqqxxxzzzzzwwwBBBBAApb egfkllqqxxxzzzzzwwwBBBBAApb egfkllqqxxxzzzzzwwwBBBBAApb egfkllqqxxxzzzzzwwwBBBBAApb egfknnnssssssssswwwBBBBAApb egfknnnssssssssswwwBBBBAApb egfknnnssssssssswwwvvvvvvpb egfknnnrrrrruuuuuuuvvvvvvpb egfknnnrrrrruuuuuuuvvvvvvpb egfknnnrrrrruuuuuuuvvvvvvpb egfknnnrrrrrtttttttttttttpb egfknnnrrrrrtttttttttttttpb egfkooooooooooooooooooooopb egfkmmmmmmmmmmmmmmmmmmmmmmb egiiiiiiiiiiiiiiiiiiiiiiiib ehhhhhhhhhhhhhhhhhhhhhhhhhb ccccccccccccccccccccccccccc a(27)=7; 34 rectangles; aaaaaaaaaaaaaaaaaaaaaaaaghb eeeeeeeeeeeeeeeeeeeqqqrpghb duuuuuuuuuuuuuuuuuuqqqrpghb dwwwwwwwwwwwwxxxxxxqqqrpghb dwwwwwwwwwwwwxxxxxxqqqrpghb dvvvvvvvvvyyyxxxxxxqqqrpghb dvvvvvvvvvyyyxxxxxxqqqrpghb dfoonzzAAAyyyDDDDEEEEErpghb dfoonzzAAAyyyDDDDEEEEErpghb dfoonzzAAAyyyDDDDEEEEErpghb dfoonzzAAAyyyDDDDEEEEErpghb dfoonzzAAAyyyDDDDEEEEErpghb dfoonzzAAACCCCCCCCFFFFrpghb dfoonzzAAACCCCCCCCFFFFrpghb dfoonzzAAACCCCCCCCFFFFrpghb dfoonzzBBBBBHHHHHHFFFFrpghb dfoonzzBBBBBHHHHHHFFFFrpghb dfmmnzzBBBBBHHHHHHFFFFrpghb dfmmnzzBBBBBGGGGGGGGGGrpghb dfmmntttttttGGGGGGGGGGrpghb dfmmntttttttssssssssssspghb dfmmntttttttssssssssssspghb dfmmnllllllllllllllllllllhb dfmmnjjjjjjjjjjjjjjjjjjjjjb dfmmniiiiiiiiiiiiiiiiiiiiii dfmmkkkkkkkkkkkkkkkkkkkkkkk dfccccccccccccccccccccccccc a(28)=7; 32 rectangles; aaaaaaaaaaaaaaaaaaaaaaaaaaab enppmmdddddddddddddddddddddb enppmmqqqrrrrlllllllllllljgb enppmmqqqrrrrlllllllllllljgb enppmmqqqrrrrtttttttuusskjgb enppmmqqqrrrrtttttttuusskjgb enppmmqqqrrrrtttttttuusskjgb enppmmqqqrrrrwwwwvvvuusskjgb enppmmqqqrrrrwwwwvvvuusskjgb enppmmxxxxxxxwwwwvvvuusskjgb enppmmxxxxxxxwwwwvvvuusskjgb enppmmxxxxxxxwwwwvvvuusskjgb enppmmxxxxxxxwwwwvvvuusskjgb enppyyyyyyyyyyyyyvvvuusskjgb enppyyyyyyyyyyyyyvvvuusskjgb enzzzzzzEEEEEEEEEEEEEEsskjgb enzzzzzzEEEEEEEEEEEEEEsskjgb enzzzzzzCCCCCCCCCCCDDDDDkjgb enzzzzzzCCCCCCCCCCCDDDDDkjgb enBBBBBBBBFFFFFFFFFDDDDDkjgb enBBBBBBBBFFFFFFFFFDDDDDkjgb enBBBBBBBBFFFFFFFFFDDDDDkjgb enAAAAAAAAAAAAAAAAAAAAAAkjgb eoooooooooooooooooooooookjgb hhhhhhhhhhhhhhhhhhhhhhhhkjgb iiiiiiiiiiiiiiiiiiiiiiiiijgb ffffffffffffffffffffffffffgb cccccccccccccccccccccccccccc a(29)=7; 34 rectangles; aaaaaaaaaaaaaaaaaaaaaaaaaaefb dilllllllllllllllllllllllmefb diknnnnnnnnnnnnnnnnnnnnnnmefb dikjtttttwwwwwwwwwwwwwwxxmefb dikjtttttwwwwwwwwwwwwwwxxmefb dikjtttttvvvvvvvAABBBzzxxmefb dikjtttttvvvvvvvAABBBzzxxmefb dikjtttttvvvvvvvAABBBzzxxmefb dikjuuuuuuuuDDDDAABBBzzxxmefb dikjuuuuuuuuDDDDAABBBzzxxmefb dikjuuuuuuuuDDDDAABBBzzxxmefb dikjssEEEEEEDDDDAABBBzzxxmefb dikjssEEEEEEDDDDAABBBzzxxmefb dikjssEEEEEEDDDDAACCCzzxxmefb dikjssEEEEEEDDDDAACCCzzxxmefb dikjssGGGHHHHHHHAACCCzzxxmefb dikjssGGGHHHHHHHAACCCyyyymefb dikjssGGGHHHHHHHAACCCyyyymefb dikjssGGGHHHHHHHAACCCyyyymefb dikjssGGGFFFFFFFFFCCCyyyymefb dikjssGGGFFFFFFFFFCCCyyyymefb dikjssGGGFFFFFFFFFCCCyyyymefb dikjssqqqqqqqqqqqqqqqqqqqqqfb dikjrrrrrrrrrrrrrpppppppppppb dikjrrrrrrrrrrrrrpppppppppppb dikjoooooooooooooooooooooooob dikjggggggggggggggggggggggggg dihhhhhhhhhhhhhhhhhhhhhhhhhhh dcccccccccccccccccccccccccccc |
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2017-01-05, 17:56
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#41 |
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Nov 2016
24 Posts |
Many of those are unexpectedly wild. I didn't foresee the variant solution for 18 to have such a range.
I imagine the ranges for the standard problem will be much tamer by comparison. |
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2017-01-07, 00:22
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#42 |
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Nov 2016
24 Posts |
Your solution for a(26) here uses each rectangle exactly twice, with all in different orientations. I have a similar solution for a(10), and no others.
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2017-09-17, 15:44
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#43 |
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Sep 2017
Belgium
1 Posts |
Please consider posting your results on this website, where you can compete for the best tiling.
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2018-06-17, 23:32
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#44 |
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Jun 2018
1 Posts |
It may be a good idea to keep track of the amount of rectangles used to create the squares. The values for the area will most likely be close to the value of the area of the square divided by the number of squares as we are looking for the closest values of area. This could potentially lead to some sort of correlation.
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