Photo:Muffet/flickr (CC-attribution)
This week, we needed your help finding a bottle of alcoholic cider in a batch of 1001 mostly non-alcoholic bottles. Due to some poor wording on my part, I accepted several different answers as possible solutions. Congratulations to Lt. Griffith for having his correct answer chosen to be this week’s winner of a $50 gift certificate from ThinkGeek!
Puzzle:
Two days before the big high school party, the parent organizers had unloaded 1000 bottles of sparkling cider and had hidden them in a locked storage closet at the school. At lunch time the day of the party, one of the teachers noticed that the door to the storage closet was opened. After investigating, the parent discovered that there were 1001 identical bottles and that all of the labels had been removed and tossed in the trash. One of the labels indicated that it belonged to a bottle of alcoholic cider rather than non-alcoholic cider. There are more than a dozen parent and teacher volunteers, all of whom are teetotalers who would get drunk on a single sip of hard cider. Strangely, it would take two hours for any of them to exhibit signs of drunkenness; they have five hours before the party starts. There’s not enough time for one person to go through and taste from all 1001 bottles. Each of the volunteers claims to be very busy with other preparations and doesn’t want to spend a lot of time on this or to drink much cider just before the party, but they all want the hard cider to be found and removed.
Given the time constraint, what is the smallest number of volunteers needed to find the alcoholic cider, and how would you do it?
Solution
From my knowledge of brewing hard cider (along with beer and wine) the best way to solve this problem is recognizing the different specific gravity of the hard cider. The yeast consumes the sugar in the cider and produces alcohol which is less dense than the original cider. A variant of specific gravity could be found by one volunteer in a couple of different ways. One, weigh a case of the cider one at a time and see if a case comes up light, then investigate the mass of the individual bottles. Or throw the bottles into a tub of water because the hard cider will be lighter (more buoyant) than the others.
Another solution was to treat this as a binary numbering problem and have 10 tee-totaling volunteers stand in as bits and number and then distribute the 1001 bottles as follows:
bottle 1 = 0000000001
…
bottle 254 = 0011111110
…
bottle 723 = 1011010011
…
bottle 1001 = 1111101001
where a “0” indicates that the volunteer in the specified bit position does not receive a sip and a “1” indicates that the volunteer does receive a sip. The combination of drunken volunteers will be unique and will give you the number of the alcoholic bottle. This is popularly known as the poison bottle riddle.
Thanks for playing! Visit ThinkGeek and enter GEEKPUZZLER for your $10 discount on a $40 or more purchase.
One of the submitters asked me about brewing and its appropriateness with young children. Since I’m an avid beer (and cider, and wine, and soda, and…) brewer, I’ll answer this question with my opinion(s) in another post (probably tomorrow).
