Occasional Puzzles - Three logicians walk into a bar...
Today’s Puzzle
Three logicians walk into a bar. The bartender asks, “Do all three of you want a drink?”
The first logician says, “I don’t know.”
The second logician says, “I don’t know.”
What does the third logician say?
Thursday’s Puzzle - Oaky, with a hint of…poison?
Recent PhD grad Raphaël plans to have a party (appropriately socially distanced, bien sûr) with 1,000 bottles of fine French wine. The party is planned for a week from today.
But there’s a problem. Raphaël has just discovered that one of the bottles is poisoned, and he doesn’t know which one. The poison has no test and no antidote; it is flavorless, odorless, and otherwise undetectable. Anyone who drinks from the poisoned bottle now will drop dead in exactly one week - just before the party.
Fortunately, Raphaël has ten loyal undergrads who are willing to sacrifice their lives to make sure the party goes off without a hitch. Using these ten undergrads and the mathematical superpowers granted by the conferral of his PhD, how does he identify the poisoned bottle before the party?
[SPOILER] Answer to Thursday’s Puzzle
The key here is to make a unique combination of tasters for each bottle of wine, so that the specific group that dies identifies the poisoned bottle. Given ten tasters, you can make 1,024 unique combinations (2^10), which is more than enough to cover all 1000 bottles of wine.
Another way to think about this is counting in binary. You have ten tasters, each of whom either did (1) or did not (0) taste a bottle of wine. Let’s say only the first two tasted a given bottle. You could represent that bottle as 0000000011. If the seventh and third tasted a given bottle, you’d represent that bottle as 0001000100. With ten digits, you can count up to 1,024 in binary, so each bottle would get a unique label corresponding to the group of undergrads that tasted it.
(Raphaël would like to note that he wouldn’t put his actual undergrads through this ordeal, but if absolutely had to, he would at least make sure they were of legal drinking age.)