Konstantin Knop posted the following puzzle on Facebook.
Puzzle. An agent sends messages to the command center. The messages have to be encrypted as a stream of 512 characters that can only be zeros and ones. Unfortunately, his transmitter is malfunctioning and gobbles 16 characters of each message. The missing 16 characters are always in the same positions in any message. As a result, the command center receives a sequence of 496 bits. Neither the center nor the agent knows which 16 bits of the sequence are eaten up by the device.
They cannot replace the broken transmitter. However, they can agree ahead of time to send K test messages, the content of which they both know. Find the smallest possible K needed to determine the positions of the disappearing 16 bits.