How can you relabel the cartons correctly if all you're allowed to do is close your eyes, reach into one carton, take out one packet, and then look at it?

You already know the carton mislabeledmustard and ketchup packetsmust contain only mustard packets or only ketchup packets. If the packet you open is mustard, you should relabel the carton you took it frommustard packets.Since you've already used up the labelmustard packets,the carton mislabeledketchup packetscannot possibly contain only mustard packets; since it is mislabeled, it can't contain only ketchup packets; so you should relabel itmustard and ketchup packets.Therefore, the remaining carton to be relabeled as ketchup packets; it's the only possibility left.

or

You already know the carton mislabeledmustard and ketchup packetsmust contain only mustard packets or only ketchup packets. If the packet you open is ketchup, you should relabel the carton you took it fromketchup packets.Since you've already used up the labelketchup packets,the carton mislabeledmustard packetscannot possibly contain only ketchup packets; since it is mislabeled, it can't contain only mustard packets; so you should relabel itmustard and ketchup packets. Therefore, the remaining carton to be relabeled asmustard packets; it's the only possibility left.

Based on a brainteaser posted on April 8, 1999, onwww.brainteasers.net.