One poisoned bottle in a thousand
Exactly one of 1000 bottles of wine is poisoned. Even a drop of the poison kills, but only after 24 hours, and the bottle must be found by then, so there is time for just one round of tasting. Each taster may take a sip from as many bottles as they like, all at the same time.
What is the smallest number of tasters that always identifies the poisoned bottle?
Fractions, decimals with at least 3 significant digits, and expressions such as sqrt(2)/2, e^-1 or pi/4.
After 24 hours, each taster is either alive or dead. How many different outcomes can tasters produce?
Number the bottles and write the numbers in binary.
h
s Shown after a correct answer. Revealing it first marks the problem as seen, not solved.
Idea. Each taster gives one bit of information: alive or dead. Ten bits are enough to name one of 1000 bottles, and nine are not.
Lower bound. With tasters there are at most possible outcomes (each taster alive or dead). Different bottles must lead to different outcomes, so . Since , at least tasters are needed.
Ten tasters are enough. Number the bottles to and write each number in binary with 10 digits, since . Taster sips from every bottle whose binary number has a 1 in position .
After 24 hours, write a 1 in position if taster died and a 0 otherwise. A taster dies exactly when the poisoned bottle has a 1 in their position, so the 10 digits spell out the number of the poisoned bottle.
So the answer is 10 tasters.