I think Thomas meant that he hoped to waste only 13 non-poisoned bottles. How many 15-sets does it take to cover all the 2-sets out of 1000? On Thu, Nov 29, 2012 at 12:46 PM, Michael Kleber <michael.kleber@gmail.com>wrote:
On Thu, Nov 29, 2012 at 11:53 AM, Thomas Colthurst <thomaswc@gmail.com
wrote:
I've been playing with these because I really want to find an unique
union
code for n=15 of size >1000 (i.e., show that you can uniquely identify the two poisoned wine bottles with only 15 bottles).
That's below the information-theoretic minimum. There are 1000-choose-2 = 499500 pairs of wine bottles; only with 19 rats could the 2^19 = 524288 outcomes possibly pick out a unique one.
--Michael
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