On Tue, 6 Dec 2011, math-fun-request@mailman.xmission.com wrote:
Date: Tue, 6 Dec 2011 16:17:33 -0800 (GMT-08:00) From: Dan Asimov <dasimov@earthlink.net> To: math-fun <math-fun@mailman.xmission.com> Subject: Re: [math-fun] Counting problem Message-ID: <10736092.1323217054054.JavaMail.root@elwamui-norfolk.atl.sa.earthlink.net>
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Ha -- and in my spare moments today I counted 87 (by hand).
So, can we split the difference and agree on 86 ?
--Dan
Allan wrote:
<< As luck would have it, this afternoon I had a boring staff meeting in which I enumerated all of them ... I think. And the answer is 85 ... I think.
I found 88. Here they are. Where is my mistake? (Each string has 3 for a 30 degree angle, 6 for 60, 9 for 90. These are the lexicographically smallest representatives of their equivalence classes.) 333333333333 33333333336 3333333339 3333333366 3333333636 333333369 3333336336 333333639 333333666 33333399 3333363336 333336339 333336366 33333669 33333696 33333939 3333633336 333363339 333363366 333363636 33336369 33336396 33336639 33336666 3333699 33339339 3333969 333633366 333633636 33363369 33363396 33363639 33363666 33363936 3336399 33366339 33366366 3336669 3336696 3336939 33393339 3339369 333999 336336336 33633639 33633666 3363399 33636339 33636366 33636636 3363669 3363696 3363939 3363966 33663366 3366369 3366396 3366639 3366666 336699 3369339 336969 336996 3393639 339399 339669 36363636 3636369 3636639 3636666 363699 363969 3663666 366399 366669 366696 366939 366966 369369 369396 369639 36999 393939 39699 666666 66699 66969 9999 -- Tom Duff. Without the Daemons, there ARE no Penguins.