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Sixteen bottles of wine riddle

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Re: Sixteen bottles of wine riddle

#3

Post by alkyon »

I wasn't familiar with 'Poison and Rat' puzzle that the post mentions as an inspiration of the title riddle.

Without looking at the answer I came up with a geometric interpretation of it (explained below as this is a spoiler to the Poison and Rat puzzle).

Re: Sixteen bottles of wine riddle

#4

Post by alkyon »

alkyon wrote: post #3

I wasn't familiar with 'Poison and Rat' puzzle that the post mentions as an inspiration of the title riddle. Without looking at the answer I came up with a geometric interpretation of it (explained below as this is a spoiler to the Poison and Rat puzzle).

Obviously 1000 rats is a wrong solution, you could remove one and still get the answer. But we could get better than that when you think about a thousand as three dimensional cube (10^3). Treating a rat with just one layer of the cube we could optimize to 30 rats. At this point I looked the answer they suggested and it was 10 (binary representation). Obviously one can construct a mulitdimensional cube with just two as a base - 2^10 and then its 20 rats. But know I realized I forgot the very first optimization I mentioned here that you could just use 1000-1 rat in the first place. So it will be fine with just (2-1)x10 rats (and 30-3=27 rats in the case of plain 3-dimensional cube).

Re: Sixteen bottles of wine riddle

#6

Post by anArbitraryOne »

How about this (choices are random): 1) Choose two bottles and one device 2) Measure the two. If they're the same, choose another device, if they're different, choose another bottle When bottles appear identical, make more measurements with different detectors on them (there's no way around doing that) When a device has accumulated n/2 0 or 1 measurements, the remainder are the opposite number (call this column constraint as per your table) When selecting the next detector, prefer the one that is closest to meeting the column constraint (otherwise choose randomly)

Sorry about the poor formatting of the algorithm but I'm typing on my phone and don't want to submit something AI generated

I was trying to figure out the runtime of this…it captures your best case scenario, and I think the worst as well, but what about the average?

Re: Sixteen bottles of wine riddle

#8

Post by gcanyon » 

   The wines are from different years
   If you apply an arbitrary order to the bottles, the number of possible year-arrangements of the bottles is 16!
   Each test gives you one bit of information
   Since 2^50 is only greater than 16! by about 50x

Re: Sixteen bottles of wine riddle

#9

Post by fainpul »

jeffwass wrote: post #2

> You briefly wonder how she managed to procure wine from over 2000 years ago before recalling that the wine cellar was built deep inside of a hypothetical scenario. Lol

Could just label the years 2000 - 2015. It just says "sixteen possible years", not where these years are on the timeline.
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