Veit, how did you even notice that symmetry in the first place? Short of applying all 10! permutations to the bit strings to see what fixes the overall code, it seems hard to stumble across... --Michael On Fri, Jan 4, 2013 at 5:24 AM, Phil Carmody <thefatphil@yahoo.co.uk> wrote:
Veit Elser <ve10@cornell.edu> wrote:
After three hours wax-&-wane found the following 50/4 code:
{225, 593, 92, 198, 394, 46, 553, 291, 816, 674, 538, 320, 780, 114, \ 53, 147, 75, 660, 897, 281, 141, 104, 278, 69, 208, 712, 420, 612, \ 578, 64, 160, 24, 6, 513, 400, 261, 48, 136, 516, 3, 640, 36, 296, 9, \ 770, 18, 528, 130, 33, 12}
I used d=6 for a slightly deeper, less greedy search. ... I am now intrigued to see what other symmetries might turn up -- recall that wax-&-wane makes no symmetry restrictions whatsoever.
I can't construct an argument in my head why more or less symmetry should be favoured. There are vastly more random sets than patterned ones, but the property being searched for requires cooperation between the members. Which of those things will have the greater influence?
So now we can evenly divide up the 1000 bottles into 50 sets of 20 from which at most 80 must be rejected.
Fantastic work! You've certainly deserved your extra bottle!
One thing that I've not seen mention of is the cost in bottles of the test on the rats. Are we assuming that the tests are such a small sample that they don't reduce the amount available for humans? Or do we need to sacrifice one bottle per set? If the latter, then there are diminishing returns, and we may have bottomed out already.
Phil
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